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For the general linear hypothesis testing problem for high-dimensional data, several interesting tests have been proposed in the literature. Most of them have imposed strong assumptions on the underlying covariance matrix so that their test statistics under the null hypothesis are asymptotically normally distributed. In practice, however, these strong assumptions may not be satisfied or hardly be checked so that these tests are often applied blindly in real data analysis. Their empirical sizes may then be much larger or smaller than the nominal size. For these tests, this is a size control problem which cannot be overcome via purely increasing the sample size to infinity. To overcome this difficulty, in this paper, a new normal-reference test using the centralized L 2 -norm based test statistic with three cumulant matched chi-square approximation is proposed and studied. Some theoretical discussion and two simulation studies demonstrate that in terms of size control, the new normal-reference test performs very well regardless of if the high-dimensional data are nearly uncorrelated, moderately correlated, or highly correlated and it outperforms two existing competitors substantially. Two real high-dimensional data examples motivate and illustrate the new normal-reference test. [ABSTRACT FROM AUTHOR]

Health condition assessment is the basis for formulating and optimizing maintenance strategies of complex systems, which is crucial for ensuring the safe and stable operation of these systems. In complex system health condition assessment, it is not only necessary for the model to handle various uncertainties to ensure the accuracy of assessment results, but also to have a transparent and reasonable assessment process and interpretable, traceable assessment results. belief rule base (BRB) has been widely used as an interpretable modeling method in health condition assessment. However, BRB-based models currently face two issues: (1) inaccuracies in expert-provided parameters that can affect the model's accuracy, and (2) after model optimization, interpretability may be reduced. Therefore, this paper proposes a new method for complex system health condition assessment called interpretable BRB with reference value optimization (I-BRB). Firstly, to address the issue of inaccurate reference values, a reference value optimization algorithm with interpretability constraints is designed, which optimizes the reference values without compromising expert knowledge. Secondly, the remaining parameters are optimized using the projection covariance matrix adaptation evolution strategy (P-CMA-ES) with interpretability constraints to improve the model's accuracy. Finally, a case study evaluating the bearing components of a flywheel system is conducted to validate the proposed method. Experimental results demonstrate that I-BRB achieves higher accuracy in health condition assessment. [ABSTRACT FROM AUTHOR]

This paper presents a wideband signal (WS) beamforming method based on Inception convolutional neural network (ICNN), named as WS-ICNN algorithm. Firstly, an Inception module is constructed via some convolutional layers with feature maps of different sizes and a pooling layer. It can not only extract different scale information of covariance matrix, but also excavate the spatial correlation information about received wideband signals, so that the inception module can help neural network improve the beamforming output performance. On this basis, an ICNN model is established, which is suitable for wideband beamforming. Then, in order to obtain a good training label for the proposed ICNN model, a taper matrix and a second-order cone programming problem are introduced to calculate a wideband beamforming weight vector label. Based on this label, the training process of the proposed ICNN model is accomplished. Finally, the well-trained ICNN model accepts the input of the covariance matrix, and output the beamforming weight vector. Simulation results demonstrate the performance of the proposed algorithm in the cases of direction-of-arrival estimation error and sensor position error. [ABSTRACT FROM AUTHOR]

To address the issue of performance degradation in the Capon beamformer when the desired signal appears in the training data, the integration operation is introduced for the interference-plus-noise covariance matrix reconstruction, and the steering vector (SV) is estimated by solving a convex optimization problem in some robust adaptive beamforming papers. However, this approach suffers from high computational complexity and is limited by the resolution of the Capon spectrum. In light of this, our paper proposes a novel robust adaptive beamforming method. To overcome the limited resolution of the Capon spectrum, we introduce the multiple signal classification method to acquire the nominal SVs. Subsequently, the SVs are updated based on subspace orthogonality. The proposed method constructs orthogonal components from the nominal SVs to circumvent the convex problem and reduce computational complexity. Additionally, the interference powers are obtained using the Capon spectrum without the noise component via eigenvalue decomposition. This refinement improves the accuracy of the estimated interference powers. Simulation results demonstrate that the proposed method is effective and robust against common mismatch errors. [ABSTRACT FROM AUTHOR]

The author discusses a study by researchers Hao Wu and Michael W. Browne, on approach to specificy error in moment structure analysis. Topics dicussed include chalanges in interpreting specification error as a second-level variation of the sample covariance matrix, emergence of no other model evaluation statistic from Broene's approach and emergence of the Root Mean Square Error of Approximation RMSEA as the natural descriptor of the "distance" between the actual and a hypothetical population.

Correlation diagnosis in multivariate process quality management is an important and challenging issue. In this paper, a new diagnostic method based on quality component grouping is proposed. Firstly, three theorems describing the properties of the covariance matrix of multivariate process quality are established based on the statistical viewpoint of product quality, to prove the correlation decomposition theorem, which decomposes the correlation of all the quality components into a series of correlations of components pairs, and then by using the factor analysis method, all quality components are grouped in order to maximize the correlations in the same groups and minimize the ones between different groups. Finally, on the basis of correlations between different groups are ignored, T2 control charts of component pairs in the same groups are established to form the diagnostic model. Theoretical analysis and practice prove that for the multivariate process quality whose the correlations between different components vary considerably, the grouping technique enables the size of the correlation diagnostic model to be drastically reduced, thus allowing the proposed method can be used as a generalized theoretical model for the correlation diagnosis. [ABSTRACT FROM AUTHOR]

In this paper, we present a statistical approach to evaluate the relationship between variables observed in a two-factors experiment. We consider a three-level model with covariance structure Σ ⊗ Ψ 1 ⊗ Ψ 2 , where Σ is an arbitrary positive definite covariance matrix, and Ψ 1 and Ψ 2 are both correlation matrices with a compound symmetric structure corresponding to two different factors. The Rao's score test is used to test the hypotheses that observations grouped by one or two factors are uncorrelated. We analyze a fermentation process to illustrate the results. Supplementary materials accompanying this paper appear online. [ABSTRACT FROM AUTHOR]

In this paper, we consider optimal portfolio selection when the covariance matrix of the asset returns is rank-deficient. For this case, the original Markowitz' problem does not have a unique solution. The possible solutions belong to either two subspaces namely the range- or nullspace of the covariance matrix. The former case has been treated elsewhere but not the latter. We derive an analytical unique solution, assuming the solution is in the null space, that is risk-free and has minimum norm. Furthermore, we analyse the iterative method which is called the discrete functional particle method in the rank-deficient case. It is shown that the method is convergent giving a risk-free solution and we derive the initial condition that gives the smallest possible weights in the norm. Finally, simulation results on artificial problems as well as real-world applications verify that the method is both efficient and stable. [ABSTRACT FROM AUTHOR]

The classical Hotelling's T 2 test and Bayesian hypothesis tests breakdown for the problem of comparing two high-dimensional population means due to the singularity of the pooled sample covariance matrices when the model dimension p exceeds the sample size n. In this paper, we develop a simple closed-form Bayesian testing procedure based on a split-and-merge technique. Specifically, we adopt the subspace clustering technique to split the high-dimensional data into lower-dimensional random spaces so that the Bayes factor can be implemented. Then we utilize the geometric mean to merge the results of the Bayesian test to obtain a novel test statistic. We carry out simulation studies to compare the performance of the proposed test with several existing ones in the literature. Finally, two real-data applications are provided for illustrative purposes. [ABSTRACT FROM AUTHOR]

High precision is a very important index in target tracking. In order to improve the prediction accuracy of target tracking, an optimized Kalman filter approach based on improved Gray Wolf algorithm (IGWO-OKF) is proposed in this paper. Since the convergence speed of traditional Gray Wolf algorithm is slow, meanwhile, the number of gray wolves and the choice of the maximum number of iterations has a great influence on the algorithm, a nonlinear control parameter combination adjustment strategy is proposed. An improved Grey Wolf Optimization algorithm (IGWO) is formed by determining the best combination of adjustment parameters through the fastest iteration speed of the algorithm. The improved Grey Wolf Optimization algorithm (IGWO) is formed, and the process noise covariance matrix and observation noise covariance matrix in Kalman filter are optimized by IGWO. The proposed approach is applied into. The experiment results show that the proposed IGWO-OKF approach has low error, high accuracy and good prediction effect. [ABSTRACT FROM AUTHOR]

Consider k independent random samples from p-dimensional multivariate normal distributions. We are interested in the limiting distribution of the log-likelihood ratio test statistics for testing for the equality of k covariance matrices. It is well known from classical multivariate statistics that the limit is a chi-square distribution when k and p are fixed integers. Jiang and Qi (Scand J Stat 42:988–1009, 2015) and Jiang and Yang (Ann Stat 41(4):2029–2074, 2013) have obtained the central limit theorem for the log-likelihood ratio test statistics when the dimensionality p goes to infinity with the sample sizes. In this paper, we derive the central limit theorem when either p or k goes to infinity. We also propose adjusted test statistics which can be well approximated by chi-squared distributions regardless of values for p and k. Furthermore, we present numerical simulation results to evaluate the performance of our adjusted test statistics and the log-likelihood ratio statistics based on classical chi-square approximation and the normal approximation. [ABSTRACT FROM AUTHOR]

Due to its non-invasiveness and easiness to implement, EEG signals decoding are in base of most based brain computer interfaces (BCI) studies. Given the non-stationary nature of these signals, a preprocessing phase is needed. An interesting idea to perform the preprocessing is the use of spatial covariance matrices. In the last years, spatial covariance matrices based preprocessing was extensively used in electroencephalography (EEG) signal processing and spatial filtering for Motor imagery (MI) BCI. Spatial covariance matrices lie in the Riemannian manifold of Symmetric Positive-Definite (SPD) matrices, therefore, the use of Riemannian geometry is attracting a lot of attention and showing to be simple, robust, and providing good performance. This paper explores the idea of enhancing the information provided to the classifier by the combination of different covariance matrices projections from their native Riemannian space to multiple class-depending tangent spaces. We demonstrate that this new approach provides a significant improvement in model accuracy. [ABSTRACT FROM AUTHOR]

Health state assessment is an important measure to maintain the safety of aerospace relays. Due to the uncertainty within the relay system, the accuracy of the model assessment is challenged. In addition, the opaqueness of the process and incomprehensibility of the results tend to lose trust in the model, especially in high security fields, so it is crucial to maintain the interpretability of the model. Thus, this paper proposes a new interpretable belief rule base model with step-length convergence strategy (IBRB-Sc) for aerospace relay health state assessment. First, general interpretability criteria for BRB are considered, and strategies for maintaining model interpretability are designed. Second, the evidential reasoning (ER) method is used as the inference machine. Then, optimization is performed based on the Interpretable Projection Covariance Matrix Adaptive Evolution Strategy (IP-CMA-ES). Finally, the validity of the model is verified using the JRC-7M aerospace relay as a case study. Comparative experiments show that the proposed model maintains high accuracy and achieves advantages in interpretability. [ABSTRACT FROM AUTHOR]

A holistic performance analysis and classification of multiport antennas (MPAs) is conducted in this paper. We focus on 5.9 GHz vehicle-to-vehicle communications suited to the emerging technology of intelligent transportation systems. Three-dimensional (3-D) uniform/isotropic, directional, and omnidirectional propagation scenarios are considered to account for any wireless environment. The presented analysis can be adapted to any MPA with an arbitrary number of ports, operating in any frequency band, or used in other emerging technologies such as in 5G and beyond 5G communications. On top of the classical key performance metrics (KPMs) in communication theory, i.e., the diversity antenna gain (DAG) and channel capacity (CC), we employ for the first time the energy efficiency as one more KPM capable to characterize performance and classify MPAs, particularly when DAG and CC fail to do so. Computation of the aforementioned KPMs departs from a covariance matrix formulation incorporating all intrinsic features that affect MPA performance, namely, MPA radiation characteristics, MPA termination conditions, and wireless propagation channel attributes. Accordingly, we derive the ideal form of the covariance matrix under the standardized and widely adopted 3-D uniform/isotropic wireless propagation scenario. A good MPA design should be one with a covariance matrix as close as possible to this ideal one. The adopted performance analysis methodology can thus inform the design of optimum MPAs and accordingly, we designed a proof-of-concept box-shaped MPA which shows outstanding performance across all propagation scenarios. It would be wise to conduct similar performance analyses as in this paper before releasing an MPA design. [ABSTRACT FROM AUTHOR]

Surrogate functions are often employed to reduce the number of objective function evaluations in a continuous optimization. However, their effects have seldom been investigated theoretically. This paper analyzes the effect of a surrogate function in the information-geometric optimization (IGO) framework, which includes as an algorithm instance a variant of the covariance matrix adaptation evolution strategy—a widely used solver for black-box continuous optimization. We derive a sufficient condition on the surrogate function for the parameter update in the IGO algorithms to point to a descent direction of the objective function expected over the search distribution. The condition is expressed in terms of three measures of correlation between the objective function and the surrogate function. Our result constitutes a partial justification for the use of a surrogate function in IGO algorithms. [ABSTRACT FROM AUTHOR]

For any machine learning model, finding the optimal hyperparameter setting has a direct and significant impact on the model's performance. In this paper, we discuss different types of hyperparameter optimization techniques. We compare the performance of some of the hyperparameter optimization techniques on image classification datasets with the help of AutoML models. In particular, the paper studies Bayesian optimization in depth and proposes the use of genetic algorithm, differential evolution and covariance matrix adaptation—evolutionary strategy for acquisition function optimization. Moreover, we compare these variants of Bayesian optimization with conventional Bayesian optimization and observe that the use of covariance matrix adaptation—evolutionary strategy and differential evolution improves the performance of standard Bayesian optimization. We also notice that Bayesian optimization tends to perform poorly when genetic algorithm is used for acquisition function optimization. [ABSTRACT FROM AUTHOR]

This paper describes the effect of analysis window functions on the performance of Mel Frequency Cepstral Coefficient (MFCC) based speaker recognition (SR). The MFCCs of speech signal are extracted from the fixed length frames using Short Time Fourier Analysis (STFA) technique where an appropriate analysis window function is required to extract frames from the complete speech signal of a speaker prior to STFA. The number of frames are consider as the number of MFCC feature vectors of a speaker which uniquely represents the speaker in feature space (domain). For the recognition purpose Vector Quantization (VQ) and/or Gaussian Mixture Model (GMM) and/or Universal Background Model GMM (UBM-GMM) based classifiers are used and a comparative study is made. Generally in state-of-the-art MFCC feature vector extraction, Hamming (in some places abbreviated as Ham in this paper) window function is used, but here we also examine the effect of other window functions like rectangular window, Hann window, B-spline windows, polynomial windows, adjustable windows, hybrid windows and Lanczos window in SR. In the present paper, we briefly describe the analysis window functions and try to evaluate text-independent speaker identification (SI). We also use voice activity detector (VAD) to discard the silence frames before STFA. Indeed, silence frames removal leads to the better performance of SR because MFCC of silent frames make the MFCC feature space intrinsic (MFCC with impurity). Here IITG MV SR database contains speech signal of speakers recorded by different devices, namely, D01, H01, T01, M01 and M02, in different environment, different language, different session. This is the reason for calling the database multi variability. It is observed that VQ classifier performs better than other GMM based classifiers for this database and the classifiers VQ-GMM, VQ-UGM-GMM and the combination of them suffers from singularity problem of covariance matrix. So we evaluate the performance of device D01 for all the classifiers and the three classifiers namely, GMM, UBM-GMM and VQ are used for the remaining four recording devices, H01, T01, M01, M02 because except these three classifiers, all other classifiers suffer from singularity problem of covariance matrix in SI. It is observed that VQ provide the highest accuracy for all the devices. [ABSTRACT FROM AUTHOR]

Manifold fitting is a manifold verification technique for data with noise and manifold structures. By extracting the expected manifold structure, the reliability of the data manifold hypothesis can be determined, and the true structure of the data without noise can conform to a manifold. This paper proposes a manifold fitting algorithm for the variable-scale spectral graph theory and estimates the deviation of the manifold structure caused by noise. Considering the scale variations in frequency-domain analysis based on spectral graph theory, details of the data under the effect of small scale and characteristics of data shape under the effect of large scale are highlighted. This study uses the average calculation and meanshift method to obtain two types of mean vectors from each neighborhood, which are essential in suppressing noise and maintaining shape, respectively. Therefore, manifold fitting is carried out from two aspects, specifically weakening noise and characterizing the manifold shape. To obtain a closer estimate of the deviation caused by noise to the manifold structure, this study also estimates the neighborhood distribution of data under the effect of medium scale, obtains the covariance information of each neighborhood, and uses the variance information to estimate the manifold structure deviations. [ABSTRACT FROM AUTHOR]

This paper proposes a lightweight bidirectional scattering distribution function (BSDF) model for layered materials with anisotropic reflection and refraction properties. In our method, each layer of the materials can be described by a microfacet BSDF using an anisotropic normal distribution function (NDF). Furthermore, the NDFs of layers can be defined on tangent vector fields, which differ from layer to layer. Our method is based on a previous study in which isotropic BSDFs are approximated by projecting them onto base planes. However, the adequateness of this previous work has not been well investigated for anisotropic BSDFs. In this paper, we demonstrate that the projection is also applicable to anisotropic BSDFs and that the BSDFs are approximated by elliptical distributions using covariance matrices. [ABSTRACT FROM AUTHOR]

Support vector regression is a promising method for time-series prediction, as it has good generalisability and an overall stable behaviour. Recent studies have shown that it can describe the dynamic characteristics of financial processes and make more accurate forecasts than other machine learning techniques. The first main contribution of this paper is to propose a methodology for dynamic modelling and forecasting covariance matrices based on support vector regression using the Cholesky decomposition. The procedure is applied to range-based covariance matrices of returns, which are estimated on the basis of low and high prices. Such prices are most often available with closing prices for many financial series and contain more information about volatility and relationships between returns. The methodology guarantees the positive definiteness of the forecasted covariance matrices and is flexible, as it can be applied to different dependence patterns. The second contribution of the paper is to show with an example of the exchange rates from the forex market that the covariance matrix forecasts calculated using the proposed approach are more accurate than the forecasts from the benchmark dynamic conditional correlation model. The advantage of the suggested procedure is higher during turbulent periods, i.e., when forecasting is the most difficult and accurate forecasts matter most. [ABSTRACT FROM AUTHOR]

In this paper, we present an unsupervised, completely blind, no-reference (NR) stereoscopic (S3D) image quality prediction model to assess the perceptual quality of natural S3D images. We study the joint dependencies between color and depth features of S3D images and empirically model these dependencies by using a bivariate generalized Gaussian distribution (BGGD). We compute the parameters of BGGD, and we also obtain the determinant and the coherence values from the covariance matrix of the proposed BGGD model. We extract the features of BGGD model and covariance matrix from the reference S3D image, followed by multivariate Gaussian (MVG) distribution modeling on the predicted features of the reference. We estimate the joint color and depth quality of the S3D images by computing the likelihood of the image features with respect to the reference MVG model. We apply the popular 2D unsupervised NIQE model on individual stereo views to estimate the overall spatial quality of the S3D images. Finally, we pool the likelihood scores and the spatial NIQE scores to achieve the estimation for the overall perceived quality of the S3D images. The performance of the proposed model is evaluated on the MICT, LIVE Phase I and II S3D image datasets. The results indicate consistent and robust performance for all datasets. Our proposed estimator is completely blind, as it requires neither training on subjective scores nor reference S3D images. [ABSTRACT FROM AUTHOR]

Adaptive EWMA (AEWMA) control charts have gained remarkable recognition by monitoring productions over a wide range of shifts. The adaptation of computational statistic as per system shift is the main aspect behind the proficiency of these charts. In this paper, a function-based AEWMA multivariate control chart is suggested to monitor the stability of the variance–covariance matrix for normally distributed process control. Our approach involves utilizing an unbiased estimator applying the EWMA statistic to estimate the process shift in real-time and adapt the smoothing or weighting constant using a suggested continuous function. Preferably, the Monte Carlo simulation method is utilized to determine the characteristics of the suggested AEWMA chart in terms of proficient detection of process shifts. The underlying computed results are compared with existing EWMA and existing AEWMA charts and proved to outperform in providing quick detection for different sizes of shifts. To illustrate its real-life application, the authors employed the concept in the bimetal thermostat industry dataset. The proposed research contributes to statistical process control and provides a practical tool for the solution while monitoring covariance matrix changes. [ABSTRACT FROM AUTHOR]

A novel online critical neural network weight adjustment algorithm is proposed in this paper by combining policy iteration and recursive least squares (RLSs) to address the problem of optimal control of players in nonlinear systems with nonzero-sum games. The interaction between players and the nonlinearity of the system make it difficult to solve the Hamiltonian function directly. From a linear regression perspective, this paper regards any admissible control and its corresponding value function as the input and output affected by perturbations. By using RLS to process the current data and store the historical data's covariance matrix to adjust the weights, the calculation is greatly simplified by avoiding the space waste caused by a lot of historical data storage and the time waste caused by data collection. When calculating the cumulative error, a discount factor is introduced to avoid the total error value tending to infinity and the effect of historical policy evaluation, where the covariance matrix tends to zero and loses its adjustment effect. When the error of the Hamiltonian equation is zero, the proposed adjustment law will also tend to zero. After that, the stability of the covariance matrix was analysed as well as the convergence of the weight errors was proved. Finally, two simulations are conducted to verify the effectiveness of the proposed algorithm based on the RLS method for solving the Nash equilibrium solution online. [ABSTRACT FROM AUTHOR]

To improve the performance of underdetermined direction of arrival (DOA) estimation in the scenario of strong mutual coupling and unknown nonuniform noise, this paper presents a novel coprime polarization sensitive array (PSA) with limited antenna number and proposes a low-complexity DOA estimation method via iterative covariance matrix reconstruction. The proposed synthetic array is composed of two single-polarized subarrays with dipole or loop antennas. Owing to the polarization domain, it can efficiently reduce the mutual coupling between subarrays, which dominates the effect of mutual coupling in the existing coprime arrays. For effectively eliminating the nonuniform noise, the cross-covariance matrix between subarrays is utilized. Based on it, the full aperture and all degrees of freedoms of the difference coarray with holes are obtained, and then, initial DOAs are estimated by using orthogonal matching pursuit algorithm. The oblique projection operators depending on initial DOAs are constructed to fill holes in difference coarray, in order to generate a larger covariance matrix for refined angle estimation. Then, a fast iterative procedure associated with covariance matrix reconstruction is given to achieve final DOA estimation, for further enhancing estimation performance. Theoretical analysis and simulation results verify the effectiveness of the proposed array and method. [ABSTRACT FROM AUTHOR]

In this paper, we consider the dynamics of Rényi negativities after a quantum quench in the free-boson chain with homogeneous dissipation. Initially we prepare the system in the squeezed thermal state, and then let it evolves under the tight-binding bosonic Hamiltonian with local linear dissipation. We use the Lindblad equation to solve the time evolution of the covariance matrix, from which one can obtain the time dependence of Rényi negativities. We are interested in the weak dissipation hydrodynamic limit where a quasi-particle picture emerges. In this limit, exact results of non-equilibrium dynamics of Rényi negativities can be obtained using the stationary phase method. We consider the Rényi negativities between both adjacent and disjoint regions in a infinite chain. We numerically test our analytical predictions and perfect matches have found. [ABSTRACT FROM AUTHOR]

The performance of adaptive beamforming will deteriorate severely under small sample support, especially when the number of snapshots is smaller than the number of sensors. In this paper, we propose an effective algorithm for robust adaptive beamforming under small sample. Firstly, we utilize standard Guassian random matrices to construct projection matrices for dimension reduction of sample covariance matrix (SCM) and steering vector (SV). Subsequently, the dimensionality-reduced SCM and SV are used to obtain more accurate Capon power spectrum in the case of small sample. By integrating the corresponding Capon power spectrum over the angular sector without desired signal, the interference-plus-noise covariance matrix (INCM) is then reconstructed. Moreover, the SV of desired signal is estimated by solving a quadratic programming problem. Finally, the weight vector of the beamformer is calculated based on the reconstructed INCM and the estimated SV. Simulation results demonstrate the effectiveness and robustness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the hypothesis testing problem of the mean vectors of high-dimensional data in the multi-sample case. We propose two maximum-type statistics and apply a parametric bootstrap technique to compute the critical values. Unlike previous hypothesis testing methods that heavily depend on the structural assumptions of the unknown covariance matrix, the proposed methods accommodate a general covariance structure. Additionally, we introduce screening-based testing procedures to enhance the power of our tests. These test procedures do not require the use of approximate limiting distributions for the test statistics. Finally, we obtain and verify the theoretical properties through simulation studies. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new scale-invariant test for linear hypothesis of mean vectors with heteroscedasticity in high-dimensional settings. Most existing tests impose strong conditions on covariance matrices so that null distributions of their tests are asymptotically normal, which restricts the application of test procedures. However, our proposed test has different null distributions under mild conditions. Additionally, the well-known Welch-Satterthwaite chi-square approximation we adopted can automatically mimic the shapes of the null distributions of the test statistic. The performances of the test are illustrated by simulation and real data in finite samples which show that it has robustness and is more powerful than three competitors. [ABSTRACT FROM AUTHOR]

One of the most relevant tasks of high-dimensional estimation is the computation of the parameters covariance matrix. This matrix offers valuable insights into the uncertainties associated with the estimation process. In the context of adaptive filtering, the weight error covariance matrix is a key parameter that determines how the filter adapts to input statistics and noise levels. Additional statistical information about the weight error vector allows one to depict a more precise description of the stochastic coupling between the adaptive weights. This paper concentrates on an in-depth study of the least mean squares asymptotic weight error covariance matrix, employing the exact expectation analysis. Through this examination, a key conclusion emerges: The symmetries commonly engendered by traditional analyses are not present in the actual covariance matrix. Instead, these symmetries are artifacts of the widespread assumption of independence. In summary, the advanced analysis performed in this work reveals a significantly more nuanced learning behavior exhibited by the least mean squares algorithm, challenging the conventional understanding put forth by traditional approaches. The theoretical predictions are confirmed by extensive simulations. [ABSTRACT FROM AUTHOR]

Spread spectrum communication is a common communication method in underwater communication. Based on the space-time processor received by the array, it can filter the signals arriving along each path separately. Combined with the diversity of space-time clusters, it can effectively improve the communication system's reliability. The core problem of the space-time processor is the direction of arrival (DOA) and signal source number estimation. Based on the good self-coherence of the spread spectrum sequence, this paper proposes a multiple signal classification algorithm (MUSIC) for accurate DOA estimation. However, since the MUSIC algorithm uses the received signal's covariance matrix for DOA estimation, the number of sources needs to be predicted in advance. Under a low signal-to-noise ratio (SNR), the signal eigenvalues and the noise eigenvalues of the covariance matrix differ slightly, which makes signal source number estimation difficult. To address this issue, a singular value decomposition method using the delay structure information of the array element is proposed to estimate the number of sources of the spreading sequence under a low SNR. The method proposed in this paper can well estimate the DOA of the signal under a low SNR. Meanwhile, there is no need to convert the signal to the individual sub-bands, which effectively reduces the calculation overhead. At the same time, the Hankel matrix is used to solve the problem that the MUSIC algorithm cannot accurately estimate the number of signal sources under the condition of low SNR. Compared with the conventional algorithm, the Hankel matrix can more accurately estimate the number of signal sources in the case of low SNR. Through simulation experiments, the effectiveness of our DOA estimation algorithm is validated under a low SNR. [ABSTRACT FROM AUTHOR]

This paper proposes a new approach for finding the conditionally optimal solution (the classifier with minimum error probability) for the classification problem where the observations are from the multivariate normal distribution. The optimal Bayes classifier does not exist when the covariance matrix is unknown for this problem. However, this paper proposes a classifier based on the constant false alarm rate (CFAR) and invariance property. The proposed classifier is optimal conditionally as it has the minimum error probability in a subset of solutions. This approach has an analogy to hypothesis testing problems where uniformly most powerful invariant (UMPI) and uniformly most powerful unbiased (UMPU) detectors are used instead of the non-existing optimal UMP detector. Furthermore, this paper investigates using the proposed classifier for modulation classification as an application in signal processing. [ABSTRACT FROM AUTHOR]

This paper analyzes the numerical stability of Markowitz portfolio optimization model, by identifying and studying a source of instability, that strictly depends on the mathematical structure of the optimization problem and its constraints. As a consequence, it is shown how standard portfolio optimization models can result in an unstable model also when the covariance matrix is well conditioned and the objective function is numerically stable. This depends on the fact that the linear equality constraints of the model very often suffer of almost collinearity and/or bad scaling. A theoretical approach is proposed that exploiting an equivalent formulation of the original optimization problem considerably reduces such structural component of instability. The effectiveness of the proposal is empirically certified through applications on real financial data when numerical optimization approaches are needed to compute the optimal portfolio. Gurobi and MATLAB's solvers quadprog and fmincon are compared in terms of convergence performances. [ABSTRACT FROM AUTHOR]

The present paper illustrates the realization of an atom-optomechanical system where an atomic ensemble is confined in a ring optomechanical cavity consisting of a fixed mirror and two movable ones. An analysis of the dynamics and the linearization of the equations allows us to derive the multimode covariance matrix. Under realistic experimental conditions, we numerically simulate the steady-state bipartite and tripartite continuous variable entanglement using the logarithmic negativity and analyze the shared entanglement in the multimode system. The introduction of the atomic medium is responsible for a more expansive plateau of entanglement indicating its robustness against temperature-induced decoherence effects. [ABSTRACT FROM AUTHOR]

Remote sensing data products often include quality flags that inform users whether the associated observations are of good, acceptable or unreliable qualities. However, such information on data fidelity is not consistently considered in remote sensing data analyses. Motivated by observations from the atmospheric infrared sounder (AIRS) instrument on board NASA's Aqua satellite, we propose a latent variable co-kriging model with separable Gaussian processes to analyze large quality-flagged remote sensing data sets together with their associated quality information. We augment the posterior distribution by an imputation mechanism to decompose large covariance matrices into separate computationally efficient components taking advantage of their input structure. Within the augmented posterior, we develop a Markov chain Monte Carlo (MCMC) procedure that mostly consists of direct simulations from conditional distributions. In addition, we propose a computationally efficient recursive prediction procedure. We apply the proposed method to air temperature data from the AIRS instrument. We show that incorporating quality flag information in our proposed model substantially improves the prediction performance compared to models that do not account for quality flags. Supplementary materials accompanying this paper appear online. [ABSTRACT FROM AUTHOR]

A fixed-effects model estimates the regressor effects on the mean of the response, which is inadequate to account for heteroscedasticity. In this paper, we adapt the asymmetric least squares (expectile) regression to the fixed-effects panel model and propose a new model: expectile regression with fixed effects (ERFE). The ERFE model applies the within transformation strategy to solve the incidental parameter problem and estimates the regressor effects on the expectiles of the response distribution. The ERFE model captures the data heteroscedasticity and eliminates any bias resulting from the correlation between the regressors and the omitted factors. We derive the asymptotic properties of the ERFE estimators and suggest robust estimators of its covariance matrix. Our simulations show that the ERFE estimator is unbiased and outperforms its competitors. Our real data analysis shows its ability to capture data heteroscedasticity (see our R package, https://github.com/amadoudiogobarry/erfe). [ABSTRACT FROM AUTHOR]

In this paper, we first construct thermofield double states for bosonic string theory in the light-cone gauge. We then obtain a coherent-thermal string state and a thermal-coherent string state. We use the covariance matrix approach to calculate the circuit complexity of coherent-thermal string states. In this approach, we generate the optimal geodesics by a horizontal string generator, and then obtain the circuit complexity using the length of the minimal geodesics in the group manifold. [ABSTRACT FROM AUTHOR]

Coherently Distributed (CD) sources are suitable for practical direction-of-arrival (DOA) estimation in massive Multiple-Input Multiple-Output (MIMO) communication systems. However, massive MIMO systems employ a large number of antennas to improve performance, which significantly raises the complexity of conventional DOA estimation algorithms for CD sources. To reduce the complexity, a novel low-complexity CD unitary estimation of signal parameters via the rotational invariance technique (U-ESPRIT) algorithm based on discrete cosine transformation (DCT) beamspace transformation and multistage Wiener filter (BU-ESPRIT) is proposed in this paper. To concentrate the signal energy and make better use of beamspace features, the DCT transformation is used to extract the signal. For the sake of reducing the complexity and achieving accurate angle estimation, U-ESPRIT is performed in beamspace. Moreover, the covariance matrix matching process and eigenvalue decomposition of the covariance matrix are substituted by forward recursion of the multistage Wiener filter to further reduce the complexity of the proposed algorithm. Theoretical analysis indicates the computational superiority of the proposed algorithm over that of some existing algorithms. Simulation results demonstrate that the proposed algorithm can be utilized to efficiently estimate angles of CD sources in massive MIMO systems. [ABSTRACT FROM AUTHOR]

In this paper, we develop a self-growing variant of the local model network (LMN) for recursive dynamical system identification. The proposed model has the following features: growing online structure, fast recursive updating rules, better memory use (no storage of covariance matrices is required), and outlier-robustness. In this regard, efficiency in performance and simplicity of implementation are the essential qualities of the proposed approach. The proposed growing version of the LMN model results from a synergistic amalgamation of two simple but powerful ideas. For this purpose, we adapt the neuron insertion strategy of the resource-allocating network to LMN model, and replaces the standard OLS rule for parameter estimation with outlier-robust recursive rules. A comprehensive evaluation involving three SISO and one MIMO benchmarking data sets corroborates the proposed approach's superior predictive performance in outlier-contaminated scenarios compared to fixed-size LMN-based models. [ABSTRACT FROM AUTHOR]

This paper is about the one-step ahead prediction of the future of observations drawn from an infinite-order autoregressive AR(∞ ) process. It aims to design penalties (fully data driven) ensuring that the selected model verifies the efficiency property but in the non-asymptotic framework. We show that the excess risk of the selected estimator enjoys the best bias-variance trade-off over the considered collection. To achieve these results, we needed to overcome the dependence difficulties by following a classical approach which consists in restricting to a set where the empirical covariance matrix is equivalent to the theoretical one. We show that this event happens with probability larger than 1 - c 0 / n 2 with c 0 > 0 . The proposed data-driven criteria are based on the minimization of the penalized criterion akin to the Mallows's C p . [ABSTRACT FROM AUTHOR]

Subspace learning of Reproducing Kernel Hilbert Space (RKHS) is most popular among domain adaption applications. The key goal is to embed the source and target domain samples into a common RKHS subspace where their distributions could match better. However, most existing domain adaption measures are either based on the first-order statistics that can't accurately qualify the difference of distributions for non-Guassian distributions or complicated co-variance matrix that is difficult to be used and optimized. In this paper, we propose a neat and effective RKHS subspace domain adaption measure: Minimum Distribution Gap (MDG), where the rigorous mathematical formula can be derived to learn the weighting matrix of the optimized orthogonal Hilbert subspace basis via the Lagrange Multiplier Method. To show the efficiency of the proposed MDG measure, extensive numerical experiments with different datasets have been performed and the comparisons with four other state-of-the-art algorithms in the literature show that the proposed MDG measure is very promising. [ABSTRACT FROM AUTHOR]

This paper explores the quaternion representation in order to devise an extended Kalman filter approach for pose estimation: inertial measurements are fused with visual data so as to estimate the position and orientation of a six degrees-of-freedom rigid body. The filter equations are described along with a data-driven tuning method that selects the model covariance matrix based on experimental results. Finally, the proposed algorithm is applied to a six degrees-of-freedom Stewart platform, a representative system of a large class of industrial manipulators that could benefit from the proposed solution. [ABSTRACT FROM AUTHOR]

Single receiver positioning has been widely used as a standard and standalone positioning technique for about 25 years. To detect the slowly growing faults caused by satellite and receiver clocks in single receiver positioning, the Autonomous Integrity Monitoring with an Extrapolation method (AIME) was proposed based on the Kalman filter measurement domain. However, AIME was designed with the assumption of there is the same number of visible satellites at each epoch, which limits its application. To address this issue, this paper proposes a state-domain Robust Autonomous Integrity Monitoring with the Extrapolation Method (SRAIME). The slowly growing fault detection statistics is established based on the difference between the estimates of the state propagator and the posterior state estimation in Kalman filtering. Meanwhile, singular value decomposition is adopted to factor the covariance matrix of the difference to increase computational robustness. Besides, the relevant formulas of the proposed method are theoretically derived, and it is proven that the proposed method is suitable for any positioning model based on the Kalman filter. Additionally, the results of two experiments indicate that SRAIME can detect slowly growing faults in single receiver positioning earlier than AIME. [ABSTRACT FROM AUTHOR]

Weber problem is an important model in facility location field, and it can be modeled as a stochastic problem when the future demand of customers is uncertain. By minimizing the maximal expectation of the objective on an ambiguity set, the distributionally robust optimization (DRO) can utilize the valuable information from historical data and thus it has become an attractive formulation for stochastic problems. In this paper, an extended moment-based DRO formulation and a polynomial-time algorithm are contributed to solving the Weber problem with uncertain demand. Specifically, by constructing a new ambiguity set, which is proved to contain the true distribution with high probability, an extended DRO formulation allowing positive semidefinite covariance matrix is first built for general stochastic problems. To obtain a more robust solution, the Weber problem is then reformulated into an equivalent stochastic variational inequality (SVI). Following the extended DRO formulation, a distributionally robust Weber problem (DRWP) is further developed with minimizing the expectation of a residual function of the SVI. The DRWP can be transformed to a semidefinite program (SDP) with an undesired exponential number of constraints. Through the adoption of a plane decomposition technique, a simple algorithm is proposed to solve the resulted SDP and obtain the optimal solution to DRWP in polynomial time. Some preliminary numerical results demonstrate the effectiveness of the proposed DRWP and algorithm. [ABSTRACT FROM AUTHOR]

This paper focuses on developing a hole-filling technique for difference co-array (DCA) of the co-prime array and its variants. In existing methods, obtaining DCA uses vectorization of the covariance matrix obtained from received signals employing Khatri–Rao product. For the co-prime array (CA) family, the DCA so obtained consists of a set of virtual contiguous elements and multiple non-uniform virtual elements. Till now, the DOA estimation from the CA family considers only virtual contiguous elements of the DCA, leaving out "holes" and other virtual non-uniform elements. This existence of holes results in a substantial decrease in consecutive degrees of freedom than expected. To address the issue of holes (in the DCA of CA family), this paper extends the original DCA of augmented CA to obtain a new virtual DCA called A C A EDCA . The A C A EDCA is virtually hole-free. Compared to DCA of the existing CA family, the resulting A C A EDCA has a larger effective DOF. Therefore, the aperture length compared to other existing variants of the co-prime array is also larger. Simulations compare performances of 9 element ACA using A C A EDCA with few other arrays of the CA family. With and without using A C A EDCA , the ACA respectively resolves 43 and 14 sources. Sliding extended CA and relocating extended CA respectively determine 22 and 25 sources. Similarly, the root-mean-square error performance of ACA using A C A EDCA is better compared to others. [ABSTRACT FROM AUTHOR]

This paper considers multistage experiments which involve, in each stage, two-level factors whose levels are hard to change. Because of such factors, in each stage, there are restrictions in the randomization of runs leading to two types of experimental units, called whole plots and split plots. As a result, there are two types of random errors, in each stage, that need to be taken into account when modeling the response variable. It is assumed that a linear mixed effects model is appropriate for analyzing observations, and that the method of generalized least squares estimation is used to obtain estimators for the fixed effects in the model. It is also assumed that the model matrix of the fixed effects is based on a general two-level fractional factorial design. The goal of this paper is to provide an analytic form of the covariance matrix of the generalized least squares estimators of the fixed factorial effects in the model, that is useful for evaluating designs. This form shows how any confounding of (fixed) effects with the whole plots, associated with the different stages, affects the variances of their generalized least squares estimators. Some special cases of this form, which correspond to a model matrix based on either a two-level regular factorial or a two-level full factorial design, are also discussed. Results can be extended to multistage experiments with randomization restrictions of the runs, in each stage, with a model matrix based on a general multilevel fractional factorial design. [ABSTRACT FROM AUTHOR]

This paper investigates the central limit theorem for linear spectral statistics of high dimensional sample covariance matrices of the form B n = n - 1 ∑ j = 1 n Q x j x j ∗ Q ∗ under the assumption that p / n → y > 0 , where Q is a p × k nonrandom matrix and { x j } j = 1 n is a sequence of independent k-dimensional random vector with independent entries. A key novelty here is that the dimension k ≥ p can be arbitrary, possibly infinity. This new model of sample covariance matrix B n covers most of the known models as its special cases. For example, standard sample covariance matrices are obtained with k = p and Q = T n 1 / 2 for some positive definite Hermitian matrix T n . Also with k = ∞ our model covers the case of repeated linear processes considered in recent high-dimensional time series literature. The CLT found in this paper substantially generalizes the seminal CLT in Bai and Silverstein (Ann Probab 32(1):553–605, 2004). Applications of this new CLT are proposed for testing the AR(1) or AR(2) structure for a causal process. Our proposed tests are then used to analyze a large fMRI data set. [ABSTRACT FROM AUTHOR]

In this paper we explore the use of a new algebraic software package in providing independent covariant proof of a conjecture in general relativity. We examine the proof of two sub-cases of the shear-free conjecture $$\displaystyle \sigma =0 {\displaystyle \, =>}\, {\displaystyle \omega }\,{\displaystyle \varTheta } =0$$ by Senovilla et al. (Gen. Relativ. Gravit 30:389-411, 1998): case 1: for dust; case 2: for acceleration parallel to vorticity. We use TensorPack, a software package recently released for the Maple environment. In this paper, we briefly summarise the key features of the software and then demonstrate its use by providing and discussing examples of independent proofs of the paper in question. A full set of our completed proofs is available online at . We are in agreeance with the equations provided in the original paper, noting that the proofs often require many steps. Furthermore, in our proofs we provide fully worked algebraic steps in such a way that the proofs can be examined systematically, and avoiding hand calculation. It is hoped that the elucidated proofs may be of use to other researchers in verifying the algebraic consistency of the expressions in the paper in question, as well as related literature. Furthermore we suggest that the appropriate use of algebraic software in covariant formalism could be useful for developing research and teaching in GR theory. [ABSTRACT FROM AUTHOR]

The paper investigates the behavior of the magnon-magnon entanglement in a double cavity-magnon system with optical parametric amplifiers (OPA) and where both cavities are coupled by the photon tunneling process. Using the standard Langevin approach, the explicit expression is suggested for the covariance matrix describing the two magnon modes and further proved by logarithmic negativity, that the steady state of the indirectly coupled magnons is genuinely entangled. Moreover, the best parameters are obtained to achieve the magnon-magnon entanglement. It is shown that the entanglement robustness against the negative effect of the thermal bath can be enhanced by a proper choice of both the cavity-cavity coupling and the OPA gain. [ABSTRACT FROM AUTHOR]

In this paper, we present an underdetermined estimation algorithm for two-dimensional (2-D) direction of arrival (DOA) based on three-parallel co-prime arrays. By exploiting the correlation among the received signals in both the time and spatial domains, a conjugate augmented spatial–temporal virtual array is constructed, which significantly increases the degrees of freedom (DOF) and expands the array aperture, effectively filling the holes within the physical array. By vectorizing the covariance matrix obtained from the spatial–temporal virtual array, we can transform the 2-D DOA estimation problem into a one-dimensional (1-D) sparse recovery problem. Thereafter, the excellent gridless methods: sparse and parametric approach (SPA) and the matrix pencil and pairing (MAPP), are adopted to efficiently resolve the 1-D sparse recovery problem, enabling the automatic pairing of the 2-D angles. And simulation results are provided to validate the enhanced accuracy of the proposed algorithm in comparison with other existing methods. [ABSTRACT FROM AUTHOR]

In this paper, we study the asymptotical behaviour of high exceedence probabilities for centered continuous R n -valued Gaussian random field X with covariance matrix satisfying Σ - R (t + s , t) ∼ ∑ l = 1 n B l (t) | s l | α l as s ↓ 0 . Such processes occur naturally as time transformations of homogenous random fields, and we present two asymptotic results of this nature as applications of our findings. The technical novelty of our proof consists in showing that the Slepian-Gordon inequality technique, essential in the univariate case, can also be successfully applied in the multivariate setup. This is noteworthy because this technique was previously believed to be inaccessible in this particular context. [ABSTRACT FROM AUTHOR]