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In this paper, we study the estimation of a block covariance matrix with linearly structured off-diagonal blocks. We consider estimation based on the least squares method, which has some drawbacks. These estimates are not always well conditioned and may not even be definite. We propose a new estimation procedure providing a structured positive definite and well-conditioned estimator with good statistical properties. The least squares estimator is improved with the use of a shrinkage method and an additional algebraic approach. The resulting so-called quasi shrinkage estimator is compared with the structured maximum likelihood estimator. [ABSTRACT FROM AUTHOR]

A Partially linear mixed effects model relating a response Y to predictors $ (X,Z,T) $ (X , Z , T) with the mean function $ X^{T}\beta +Zb+g(T) $ X T β + Zb + g (T) is considered in this paper. When the parametric parts' variable X are measured with additive error and there is ill-conditioned data suffering from multicollinearity, a new kernel two-parameter prediction method using the kernel ridge and Liu regression approach is suggested. The kernel two parameter estimator of β and the predictor of b are derived by modifying the likelihood and Henderson methods. Matrix mean square error comparisons are calculated. We also demonstrate that under suitable conditions, the resulting estimator of β is asymptotically normal. The situation with an unknown measurement error covariance matrix is handled. A Monte Carlo simulation study, together with an earthquake data example, is compiled to evaluate the effectiveness of the proposed approach at the end of the paper. [ABSTRACT FROM AUTHOR]

This paper presents a robust method for robust estimation of quadratic discriminant analysis. The mean and covariance matrix for estimating quadratic discriminant rule is computed using a robust estimation method called Sn method established from a robust covariance estimator S n C o v. The performance of the proposed method is evaluated using the results of simulated samples. This outlier detection method is compared with some well-known methods available in the current literature. The application of the proposed method in real-life data is also executed in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we develop a maintenance model for systems subjected to multiple correlated degradation processes, where a multivariate stochastic process is used to model the degradation processes, and the covariance matrix is employed to describe the interactions among the processes. The system is considered failed when any of its degradation features hits the pre-specified threshold. Due to the dormancy of degradation-based failures, inspection is implemented to detect the hidden failures. The failed systems are replaced upon inspection. We assume an imperfect inspection, in such a way that a failure can only be detected with a specific probability. Based on the degradation processes, system reliability is evaluated to serve as the foundation, followed by a maintenance model to reduce the economic losses. We provide theoretical boundaries of the cost-optimal inspection intervals, which are then integrated into the optimisation algorithm to relieve the computational burden. Finally, a fatigue crack propagation process is employed as an example to illustrate the effectiveness and robustness of the developed maintenance policy. Numerical results imply that the inspection inaccuracy contributes significantly to the operating cost and it is suggested that more effort should be paid to improve the inspection accuracy. [ABSTRACT FROM AUTHOR]

In the analysis of clustered or longitudinal data structures, such as those coming from surveys or trials, it is desirable to accurately estimate the dependence parameters within repeated measurements. Marginal models together with the generalized estimating equation allow to consistently estimate regression coefficients. Inference may be problematic for small and moderate sample sizes, or with models involving many covariates. Moreover, the correlation structure may be misspecified leading to a substantial bias in the sandwich covariance matrix estimator. The paper focuses on Gaussian with exchangeable correlation matrix model and proposes to use adjustments of the score function aiming at mean and median bias reduction of maximum likelihood estimates. Extensive simulation studies show a remarkable performance of the proposed methods. In addition, we show that the bias reduction methods maintain an appreciable robustness with respect to the maximum likelihood under misspecification of the correlation matrix. [ABSTRACT FROM AUTHOR]

In order to improve the effect of agricultural economic structure optimisation, this paper builds an agricultural economic structure optimisation analysis system based on factor analysis and intelligent algorithms, and uses a set of low-dimensional hidden factor vectors to describe the covariance matrix structure of high-dimensional observation vectors. Moreover, this paper combines the algorithm with the actual situation to obtain the optimisation analysis process of the agricultural economic structure. On this basis, this paper analyses the optimisation of agricultural economic structure in practice with a case analysis method. Moreover, this paper uses mathematical analysis to process agricultural economic structure data, and uses mathematical statistics to visualise the process of data processing. In addition, this paper combines the weighted average to perform parameter processing, combines with the comparative analysis method to obtain the agricultural economic results parameters, and analyses these parameters. Finally, on the basis of the above, this paper proposes the corresponding optimisation strategy of agricultural economic structure. The research results show that the method proposed in this paper has a certain effect. [ABSTRACT FROM AUTHOR]

In this paper, the non-fragile joint state and fault estimation problem is investigated for a class of nonlinear time-varying complex networks (NTVCNs) with uncertain inner coupling and mixed time-delays. Compared with the constant inner coupling strength in the existing literature, the inner coupling strength is permitted to vary within certain intervals. A new non-fragile model is adopted to describe the parameter perturbations of the estimator gain matrix which is described by zero-mean multiplicative noises. The attention of this paper is focussed on the design of a locally optimal estimation method, which can estimate both the state and the fault at the same time. Then, by reasonably designing the estimator gain matrix, the minimized upper bound of the state estimation error covariance matrix (SEECM) can be obtained. In addition, the boundedness analysis is taken into account, and a sufficient condition is provided to ensure the boundedness of the upper bound of the SEECM by using the mathematical induction. Lastly, a simulation example is provided to testify the feasibility of the joint state and fault estimation scheme. [ABSTRACT FROM AUTHOR]

In this paper, we put forward 'kernel Liu prediction approach' instead of 'kernel prediction approach' under multicollinearity case in partially linear mixed measurement error model. We obtain the necessary and sufficient condition for the superiority of the linear combinations of the predictors in the sense of the matrix mean square error criterion and give the selection of the Liu biasing parameter via the Conceptual Prediction ( C p ) criterion. The asymptotic normality condition is examined and the unknown covariance matrix of measurement errors circumstance is derived. We study a numerical example together with a Monte Carlo simulation study to evaluate the performance of the kernel Liu prediction approach at the end of this paper. [ABSTRACT FROM AUTHOR]

AbstractForecasts of regional electricity net-demand, consumption minus embedded generation, are an essential input for reliable and economic power system operation, and energy trading. While such forecasts are typically performed region by region, operations such as managing power flows require spatially coherent joint forecasts, which account for cross-regional dependencies. Here, we forecast the joint distribution of net-demand across the 14 regions constituting Great Britain’s electricity network. Joint modelling is complicated by the fact that the net-demand variability within each region, and the dependencies between regions, vary with temporal, socio-economic and weather-related factors. We accommodate for these characteristics by proposing a multivariate Gaussian model based on a modified Cholesky parametrisation, which allows us to model each unconstrained parameter via an additive model. Given that the number of model parameters and covariates is large, we adopt a semi-automated approach to model selection, based on gradient boosting. In addition to comparing the forecasting performance of several versions of the proposed model with that of two non-Gaussian copula-based models, we visually explore the model output to interpret how the covariates affect net-demand variability and dependencies. The code for reproducing the results in this paper is available at https://doi.org/10.5281/zenodo.7315105. [ABSTRACT FROM AUTHOR]

The traditional coprime parallel array (TrCPA) is prone to suffer from the problem of angle ambiguity, due to its larger inter-element spacing and limited array aperture, for two-dimensional direction of arrival estimation. And the classic multiple signal classification (MUSIC) algorithm has heavy complexity and has poor estimation ability in some unsatisfactory situations. Both restrict the improvement of angle estimation performance. In this paper, we design a novel displaced coprime parallel array termed NDCPA, by rearranging and misplacing all subarrays of TrCPA along the coordinate axis, which brings about larger array aperture making contributions to superior angle estimation accuracy. Besides, we propose an improved two-step reduced-dimensional MUSIC algorithm to further enhance angle estimation accuracy. The proposed method reconstructs the covariance matrix, which can fully exploit the information contained in uniform linear subarrays. Meanwhile, the transformation of angle domain divides the original two-dimensional search into two one-dimensional searches, reducing complexity to a certain extent. Finally, simulation results verify the effectiveness and applicability of the proposed configuration and method compared with the other structures and methods. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to propose a novel method (RMD-MRCD-PCA) of identification of High Leverage Points (HLPs) in high-dimensional sparse data. It is to address the weakness of the Robust Mahalanobis Distance (RMD) method which is based on the Minimum Regularized Covariance Determinant (RMD-MRCD), which indicates a decrease in its performance as the number of independent variables (p) increases. The RMD-MRCD-PCA is developed by incorporating the Principal Component Analysis (PCA) in the MRCD algorithm whereby this robust approach shrinks the covariance matrix to make it invertible and thus, can be employed to compute the RMD for high dimensional data. A simulation study and two real data sets are used to illustrate the merit of our proposed method compared to the RMD-MRCD and Robust PCA (ROBPCA) methods. Findings show that the performance of the RMD-MRCD is similar to the performance of the RMD-MRCD-PCA for p close to 200. However, its performance tends to decrease when the number of p is more than 200 and worsens at p equals 700 and larger. On the other hand, the ROBPCA is not effective for less than 20% contamination as it suffers from serious swamping problems. [ABSTRACT FROM AUTHOR]

There has been a growing interest in research regarding monitoring a process through a regression model (called a profile) rather than a simple quality characteristic. This paper proposes a new monitoring scheme to simultaneously monitor the multivariate multiple linear profiles' parameters. This scheme is based on the Shewhart control chart concept and only has one single (max-type) control chart for monitoring regression coefficients and error's variation, which uses a new statistic to improve the variability (error's variance-covariance matrix) shift detection in multivariate profiles. To increase the sensitivity and capability of the proposed scheme, especially in detecting small to moderate shift sizes, we add a variable parameters (VP) adaptive scheme to the developed control chart as well, considering that no adaptive monitoring schemes have so far been developed for monitoring the multivariate multiple linear profiles and neither are there any VP adaptive features for all profile monitoring schemes. Next, we develop a Markov chain model to compute the time to signal and run length performance measures. After that, we perform extensive numerical analyses to first compare the proposed control chart with the best available control charts and then evaluate its performance under different shift scenarios as well as different dimensions. The results show that the new monitoring scheme performs well compared to the best available monitoring schemes, and more importantly, it is more applicable in real practice. Finally, an illustrative example is presented to show the implementation of the proposed scheme in practice. [ABSTRACT FROM AUTHOR]

The classical autoregressive type models are widely used in time series modelling. Recently, a class of models known as generalized autoregressive, recognized by an additional parameter, has been proposed in order to reveal some hidden features which cannot be characterized by the standard autoregressive models. In this paper, the generalized autoregressive models are extended to the vector-valued autoregressive models which provide a flexible framework for modelling the dependent data. The properties of the new model such as stationary conditions, some explicit form of the auto-covariance function and the spectral density matrices are investigated. Unknown parameters are then estimated and compared with other kinds of traditional methods. The numerical results obtained by means of simulation studies are then reported. Finally, the traditional autoregressive model and generalized autoregressive model are fitted to a well-known bivariate time series, respectively, and the performance of the proposed models and the estimation methods are discussed. [ABSTRACT FROM AUTHOR]

In multivariate analysis, the eigenvalues of the covariance matrix are crucial. Thus, there is a demand among users to find a good, easy-to-use chi-squared approximation. However, there are few good approximations for eigenvalues. Therefore, in this paper, we focus on the chi-squared approximation, proposing a new approximation and investigating its accuracy. [ABSTRACT FROM AUTHOR]

Due to gradual disappearance of global demographic dividend, the improvement of workforce efficiency becomes increasingly important. It has been commonly recognised that workforce motivation can largely stimulate the workers, especially in manufacturing systems. This paper investigates a worker scheduling problem under given work shifts with workforce motivation effects, where motivation effects are characterised by motivation coefficients of job processing times. We focus on the situation where motivation coefficients are uncertain due to various factors, and only the mean vector and covariance matrix are known. The objective is to maximise the service level, measured by the probability of ensuring no tardy jobs. We first propose a distributionally robust chance constrained formulation with a probabilistic objective function. Then an adapted sample average approximation (SAA) method and a heuristic, based on an approximated mixed integer second-order cone programming (MI-SOCP) model and the idea of problem decomposition, is developed. Numerical results show that the decomposition-based heuristic is more efficient. We also draw some managerial insights. [ABSTRACT FROM AUTHOR]

Local covariance matrix descriptor is a new spatial-spectral feature generation method. It has been successfully applied for remote sensing image classification. Meanwhile, there are some critiques of it because it neglects nonlinear relationships between features, which are serious when applied to hyperspectral images (HSIs). So, the present paper aims to develop weighted local kernel matrix (WLKM) descriptors for the spatial-spectral classification of HSI. The developed weighted local kernel matrix features, including spectral-textural-geometrical aspects, have been used in two classification schemes proposed. In the first approach, called 'early fusion', the weighted sum of WLKM descriptors derived from spectral and spatial features is classified using the log-Euclidean kernel SVM. In the second approach, called 'late fusion', a multiple log-Euclidean kernel SVM strategy based on the WLKM descriptors of spatial and spectral features is developed for HSI classification. Experiments on three widely used HSI datasets have proved the superiority of the proposed approaches over some recent spatial-spectral HSI classification techniques. [ABSTRACT FROM AUTHOR]

Multivariate monitoring of industrial or clinical procedures often involves more than three correlated quality characteristics and the status of the process is judged using a sample of size one. Majority of existing control charts for monitoring process variability for individual observations are capable of monitoring up to three characteristics. One of the hurdles in designing optimal control charts for large dimension data is the enormous computing resources and time that is required by simulation algorithm to estimate the charts parameters. This paper proposes a novel algorithm based on Parallelised Monte Carlo simulation to improve the ability of the Multivariate Exponentially Weighted Mean Squared Deviation and Multivariate Exponentially Weighted Moving Variance charts to monitor process variability for high dimensions in a computationally efficient way. Different techniques have been deployed to reduce computing space and execution time. The optimal control limits (L) to detect small, medium and large shifts in the covariance matrix of up to 15 characteristics are provided. Furthermore, utilising the large number of optimalLvalues generated by the algorithm enabled authors to develop exponential decay functions to predictLvalues. This eliminates the need for further execution of the parallelised Monte Carlo simulation. [ABSTRACT FROM AUTHOR]

Disassembly line balancing problem (DLBP), which is to select disassembly process, open workstations and assign selected tasks to opened workstations, plays an important role in the recycling of End Of Life products. In real-world disassembly operations, task processing times are usually stochastic due to various factors. Most related works address the uncertain processing times by assuming that the probability distribution is known and the task processing times are independent of each other. In practice, however, it is difficult to get the complete distributional information and there is always underlying correlation between the uncertain processing times. This paper investigates the DLBP with partial uncertain knowledge, i.e. the mean and covariance matrix of task processing times. A new distributionally robust formulation with a joint chance constraint is proposed. To solve the problem, an approximated mixed integer second-order cone programming (MI-SOCP) model is proposed, and a two-stage parameter-adjusting heuristic is further developed. Numerical experiments are conducted, to evaluate the performance of the proposed method. We also draw some managerial insights and consider an extension problem. [ABSTRACT FROM AUTHOR]

Customer credit risk or payment probability, influenced by factors such as financial conditions and bank policies, has hindered fast Asia-Pacific economic growth. Besides, the working time is usually limited due to regulations and limited resources. Driven by profit, some jobs may be rejected on tactical level and the accepted jobs are scheduled on operational level, respecting the allowed working time. This paper studies a stochastic flowshop scheduling problem, assuming that only the mean and covariance matrix of uncertain payment probabilities and processing times are known. The objective is to maximise the profit level, i.e. the probability of the profit no less than the planned one, while controlling the risk of surpassing the limited working time. A new distributionally robust chance constrained model is proposed. The sample average approximation (SAA) method, the robust SAA method and a hierarchical approach, based on an approximated mixed integer second-order conic program, are developed. Numerical experiments show that the hierarchical approach is more efficient. Moreover, some managerial insights are drawn. [ABSTRACT FROM AUTHOR]

The portfolio optimization problem can be reformulated by a regression model. Mean-variance portfolios, which are constructed using the sample mean and covariance matrix of asset returns can be considered as a function of the ordinary least squares estimator of the linear regression coefficients. It is well known that this estimator has several drawbacks. In particular many researchers have pointed out its high sensitivity in the presence of outliers and its loss of efficiency in the presence of small deviations from the normality assumption. In this paper we propose a novel regression approach for optimizing portfolios by means of quantile regression models. The proposed portfolios are constructed using certain robust and distribution-free estimators and can be obtained by solving a single linear program, where estimation and portfolio optimization are performed in a single step. Our numerical results on simulated and empirical data confirm that the proposed portfolios behave much better than the traditional mean-variance portfolio, in terms of the Sharpe ratio and expected loss in utility. [ABSTRACT FROM AUTHOR]

AbstractToday, manufacturers face two challenges: the financial limitation of sampling and the large number of study quality characteristics. In such situations, the problem dimension is usually larger than the sample size, which is known in the literature of statistical quality control as a high dimensional process. The use of conventional multivariate charts to monitor the covariance matrix of such processes is not possible for two reasons: (1) the non-reversibility of the sample covariance matrix, (2) the possibility of the occurrence of sparse shifts in which only a few elements of the covariance matrix are affected. This paper focuses on Phase II monitoring of the covariance matrix of high-dimensional processes based on integrating the ridge penalized likelihood ratio (RPLR) statistic and the combined DS-VSS sampling method, in which DS and VSS features are used concurrently. The performance of the proposed DS-VSS RPLR control chart is compared with the RPLR one in terms of three metrics of the average run length, standard deviation of the run length, and expected value of sample size under three types of joint diagonal/off-diagonal, diagonal and off-diagonal shift patterns. The results show that the DS-VSS scheme is more sensitive than the RPLR in detecting both sparse and non- sparse changes. [ABSTRACT FROM AUTHOR]

The structure of arrays capable of receiving wideband signals differs from arrays which can only receive narrowband signals. These arrays should be capable of receiving several GHz instant bandwidth signals over the entire operating frequency, like High Resolution Radars or Terahertz in 6G communication systems. In these arrays, the number of beamformer coefficients increase due to using a time delay line structure, hence leading to a high computational complexity. This is one of the challenges of beamforming in wideband systems. Additionally, there are other factors in classic Wideband beamformers. These factors include poor performance against input DOA (direction of arrival) error, array calibration error, and too many snapshots to reach the steady state of the beamformer. Therefore, this paper focuses on the robustness of beamforming using deep learning technique, which has not been discussed before. The basis of network design is convolutional layers. Two different proposed approaches have been proposed to obtain optimal structure. In the first approach, appropriate values of hyperparameters are estimated, whereas the network model is selected in the second approach. Also, the network training method is done to become more robust against the mentioned factors. In the proposed structures, the constraints of the previous methods have been evaluated. The proposed structure is shown to have a superior performance when compared with other existing algorithms. In addition, the matrix of signal samples is replaced with the covariance matrix at the network's input, so the calculation time is significantly improved compared to the previous methods. [ABSTRACT FROM AUTHOR]

In a simultaneous localization and mapping (SLAM) system, in general, distribution estimation based on a particle filter is used for localization of Unmanned Ground Vehicle (UGV) with a laser rangefinder, and point estimation based on optimization is used for Unmanned Aerial Vehicle (UAV) with a monocular camera. In order for such robots to perform cooperative localization to improve accuracy, it is necessary to convert the localization results of point estimation and distribution estimation into a format that can be introduced to each other. In this paper, we propose an integration method of estimation results for cooperative localization by UAV and UGV. The UAV point estimation result is converted to a normal distribution by giving a fixed covariance matrix in order to introduce it as the observation likelihood of the UGV. On the other hand, the particle pose with maximum weight obtained from the UGV distribution estimation result is added to the current pose constraint in UAV optimization. As a result, this allows stable localization of both by correcting with the estimation result of the other even in an environment where either one is disadvantageous for localization. [ABSTRACT FROM AUTHOR]

It is widely recognized that the safe and robust design of a nuclear system requires an uncertainty propagation analysis concerning the various nuclear data used as input parameters, especially in view of the most recent design methodologies like the best-estimate plus uncertainty approach. The evaluation of the input uncertainties and their propagation to the design parameters of interest is particularly important in the case of nuclear fusion machines, such as the Affordable Robust Compact (ARC) reactor, which features the presence of uncommon isotopes in the nuclear engineering field, like fluorine, beryllium, and lithium. The uncertainties of the nuclear data of these nuclides can have a significant impact on the fundamental design parameters, such as the target tritium breeding ratio (TBR). Hence, in this work we investigate the application of different methods for propagating the nuclear data uncertainty to the parameters of interest, computed with the Serpent 2 Monte Carlo code. All the methods proposed in this work share the feature of being nonintrusive, implying that they can be profitably employed independently of the physical and/or computational model adopted. The methods discussed in this work are the fast Total Monte Carlo, the GRS, the unscented transform, and the polynomial chaos expansion. The first three methods led to similar values in terms of relative standard deviation of the TBR due to nuclear data and can be considered as fast alternatives to brute-force sampling methods. For these three methods, the present paper suggests how to select the best approach according to the kind of analysis to be performed and the nuclides considered in the study. The effect of the use of different nuclear data libraries and of different input covariance matrices is also examined. The main outcome of these analyses suggests that the uncertainties in the nuclear data of nickel, fluorine, beryllium, and lithium are sufficiently small (i.e., smaller than 1%) to prevent the TBR from assuming values below the design constraints. The overall uncertainty on the TBR of ARC due to the nuclides here considered was evaluated to be ~0.9%. Concerning the polynomial chaos expansion approach, this paper shows that its application is computationally inefficient compared to the other techniques when the input data dimensionality are very large, as for the case of nuclear data. [ABSTRACT FROM AUTHOR]

A commonly used test for the independence of two sets of variables from a normal multivariate population is the Wilks Lambda test or the multivariate likelihood ratio test (LRT). However, this test's performance is highly influenced by outliers and non-normality of the data and thus, robust test statistics should be used, allied to Monte-Carlo methods. In this paper, we proposed and evaluated three new likelihood ratio test for the independence of two sets of multivariate variables (LRTR, T and TR), replacing the traditional covariance matrix estimator with the robust comedian estimators. The results showed that the proposed test T and TR control type I error rates also for non-normal distributions outperforming the ordinary test. [ABSTRACT FROM AUTHOR]

Portfolio optimization relies in three main elements: the utility function, the use of multivariate dependence measure between assets and the returns of the assets. The first problem is well known in finance since one can use several different types of portfolio utility functions depending on her objective function and constraints. The two remaining problems are relevant topics of research: the measure and forecast of the dependence between assets and the forecast of the returns of assets. In this paper, we present a new method with artificial intelligence to estimate the variance and covariance matrices of financial time series data accounting for small sample size, large number of assets and presences of outliers. We compare results using different approaches, e.g., Minimum covariance determinant (MCD), Minimum Volume Ellipsoid (MVE), Minimum Regularized Covariance Determinant (MRCD) and Orthogonalized Gnanadesikan-Kettenring (OGK). The proposed approach is robust under several financial stylized facts and presents good performance with respect to the cumulative returns in the US markets (NASDAQ Stock Exchange) for 95 assets during 2015 to the beginning of 2019. These study contributes to fill in the literature gap in covariance estimation for small sample size, large number of assets and presences of outliers and contributes to investors to making better portfolio management. [ABSTRACT FROM AUTHOR]

In this paper, the problem of testing the equality of the mean vectors of k populations with possibly unknown and unequal covariance matrices is investigated in high-dimensional settings. The null distributions of most existing tests are asymptotically normal which inevitably imposes strong conditions on covariance matrices. However, we assume here only mild additional conditions on the proposed test, which offers much flexibility in practical applications. Additionally, the Welch–Satterthwaite χ 2 -approximation we adopted can automatically mimic the shape of the null distribution of the proposed test statistic, while the normal approximation cannot achieve the adaptivity. Finally, an extensive simulation study shows that the proposed test has better performance on both size and power compared with existing methods. [ABSTRACT FROM AUTHOR]

The aim of the paper is to determine maximum-likelihood estimation equations. Observations follow a multivariate normal distribution,, where,anddescribe the unknown covariance structure between rows and columns of, respectively. Imposing restrictions onandfour types of covariance structures will be considered. [ABSTRACT FROM AUTHOR]

Traces of Wishart matrices appear in many applications, for example in finance, discriminant analysis, Mahalanobis distances and angles, loss functions and many more. These applications typically involve mixtures of traces of Wishart and inverse Wishart matrices that are concerned in this paper. Of particular interest are the sampling moments and their limiting joint distribution. The covariance matrix of the marginal positive and negative spectral moments is derived in closed form (covariance matrix of Y = [ p − 1 Tr { W − 1 } , p − 1 Tr { W } , p − 1 Tr { W 2 } ] ′ , where W ∼ W p (Σ = I , n) ). The results are obtained through convenient recursive formulas for E [ ∏ i = 0 k Tr { W − m i } ] and E [ Tr { W − m k } ∏ i = 0 k − 1 Tr { W m i } ]. Moreover, we derive an explicit central limit theorem for the scaled vector Y, when p / n → d < 1 , p , n → ∞ , and present a simulation study on the convergence to normality and on a skewness measure. [ABSTRACT FROM AUTHOR]

This paper is concerned with comparison problems of predictors between a linear mixed model (LMM) that includes both fixed and random effects and its transformed model under general assumptions. Our aim is to establish a variety of equalities and inequalities for comparing covariance matrices of the best linear unbiased predictors (BLUPs) of unknown vectors under the models by using various inertia and rank formulas of block matrices. We also give some results for special transformed models such as submodels of original LMMs by applying the results obtained for general cases. [ABSTRACT FROM AUTHOR]

Because the geological conditions of the reservoir are complicated and involve many factors, the inversion of reservoir parameters is realized by using numerical simulation technology and history matching method. At present, Ensemble Kalman Filter method is widely used in history matching. But in the fact, the Ensemble Kalman Filter has problem such as inaccurate gradient calculation and pseudo correlation. In this paper, the Ensemble Kalman Filter based on shrinkage covariance matrix estimation is used to construct the localization matrix. By gradually matching production performance, the gradient of data assimilation method is corrected, the pseudo correlation is weakened, the reservoir model is updated, and the optimal estimate is obtained. By an example, we compare the Ensemble Kalman Filter and Ensemble Kalman Filter based on shrinkage covariance matrix estimation. The results show that Ensemble Kalman Filter based on shrinkage covariance matrix estimation is superior to Ensemble Kalman Filter in the accuracy of model production dynamic matching. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the simultaneous test for the high-dimensional linear model coefficient. In high-dimensional setting, the traditional F-test is infeasible while the dimension is larger than the sample size because the sample covariance matrix is not invertible. Even when the dimension is smaller than the sample size, the efficiency of the classical F-test diminishes rapidly as the dimensionality increases. Several existing methods modified the classical F-test by removing the inverse term in the statistics and performed well. However, those modifications may lose efficiency due to the ignorance of correlation and those moment based procedures are sensitive to outlying observations and heavy tailed data. We propose a centered rank based method using projection which is robust in a broad range of distribution and alternative hypothesis. Under some mild conditions, we derive the best projection direction. The proposed procedure can retain type I error rate pretty well with the asymptotic distribution due to the data splitting strategy. Finite sample simulation studies are in accordance with the theoretical results. [ABSTRACT FROM AUTHOR]

Reconstruction of missing seismic data is a critical procedure for subsequent applications like multiple wave suppression, wave-equation migration imaging and so on. In this paper, a fast, hyperparameter-free and sparse iterative spectral estimation approach is proposed for the reconstruction of two-dimensional seismic data of randomly missing traces. The proposed approach is based on the harmonic structure of the frequency slice of seismic data and the weighted covariance fitting criterion. Specifically, the method first iteratively estimates the spectrum of the frequency slice by solving a weighted covariance fitting problem. Then, the missing data is reconstructed by using the estimated spectrum and a linear minimum mean-squared error estimator. However, the spectral estimation depends on matrix-vector multiplications for each iteration, which has a high computational cost when the data increase to a large size. To solve this problem, a fast iterative technology is proposed by using an inverse fast Fourier transform, which fully exploits the Hermitian–Toeplitz structure of the covariance matrix and the exponential form of the steering vector and it significantly reduces the computational complexity. The proposed algorithm is hyperparameter-free, can provide super spectral resolution, and thus obtain better reconstruction performance. The experimental results of synthetic and real seismic data show that the proposed algorithm has higher reconstruction accuracy and lower computational complexity compared to other commonly used reconstruction algorithms. [ABSTRACT FROM AUTHOR]

For high-dimensional two-sample Behrens–Fisher problems, several non-scale-invariant and scale-invariant tests have been proposed. Most of them impose strong assumptions on the underlying group covariance matrices so that their test statistics are asymptotically normal. However, in practice, these assumptions may not be satisfied or hardly be checked so that these tests may not be able to maintain the nominal size well in practice. To overcome this difficulty, in this paper, a normal reference scale-invariant test is proposed and studied. It works well by neither imposing strong assumptions on the underlying group covariance matrices nor assuming their equality. It is shown that under some regularity conditions and the null hypothesis, the proposed test and a chi-square-type mixture have the same normal and non-normal limiting distributions. It is then justifiable to approximate the null distribution of the proposed test using that of the chi-square-type mixture. The distribution of the chi-square type mixture can be well approximated by the Welch–Satterthwaite chi-square-approximation with the approximation parameter consistently estimated from the data. The asymptotic power of the proposed test is established. Numerical results demonstrate that the proposed test has much better size control and power than several well-known non-scale-invariant and scale-invariant tests. [ABSTRACT FROM AUTHOR]

This paper presents a new methodology for detecting bare rough soil in non-urban areas using synthetic aperture radar data. Our approach involves matching the covariance/coherence matrix to the extended Bragg (xBragg) model. Our method uses automatic OTSU's thresholding based on roughness angles histogram to determine output classes and avoid complex calculations, making it suitable for onboard computing. The procedure is suitable for a range of soil roughness but not for highly specular surfaces. The performance of the suggested methodology was evaluated using simulated data and real L- and P-band SAR datasets from two different sites with various features. Our results demonstrate the effectiveness of the method for rough agricultural and natural surfaces, with good performance and a success rate of up to about 95 % across a wide range of roughness values from 0 ∘ to 65 ∘ . [ABSTRACT FROM AUTHOR]

This paper is concerned with the variance-constrained filtering problem for a class of discrete-time genetic regulatory networks (GRNs) with state delay and random one-step measurement delay. The phenomenon of the random one-step measurement delay is characterised by a random variable, which is assumed to obey the Bernoulli distribution with known occurrence probability. The purpose of the addressed problem is to design a filter such that, in the presence of state delay and random one-step measurement delay, an upper bound of the filtering error covariance matrix can be obtained and the explicit expression of the filter gain matrix is given. Then, the proposed variance-constrained filtering method can be used to approximate the concentrations of mRNAs and proteins. Finally, a numerical example is provided to illustrate the effectiveness of the designed filtering scheme. [ABSTRACT FROM AUTHOR]

This paper develops an efficient Exponential Twisting Importance Sampling technique for variance reduction when it is used to price financial derivatives. A general class of exponential change of measure is well explored. This is the generalization of the proportional exponential twisting function, , discussed as an Example 4.6.2 in Glasserman's book (2004). Then a new framework to find the optimal importance sampling density function is proposed based on the Cauchy-Schwartz Inequality and the Least Square Approach. In the special Gaussian case, the theory of our general exponential change of measure means finding the new drift vector and covariance matrix simultaneously. The method proposed by the paper has little smoothness requirements for the payoff functions and doesn't rely on the initial values. It is illustrated that this method is high efficient for pricing financial derivatives, such as Asian options, Straddle options, Volatility derivatives and the pricing under the stochastic volatility models. Furthermore, this method can be extended to more general importance sampling densities such as non-Gaussian or multi-modal distributions. [ABSTRACT FROM AUTHOR]

Stochastic scheduling optimisation is a hot and challenging research topic with wide applications. Most existing works on stochastic parallel machine scheduling address uncertain processing time, and assume that its probability distribution is known or can be correctly estimated. This paper investigates a stochastic parallel machine scheduling problem, and assumes that only the mean and covariance matrix of the processing times are known, due to the lack of historical data. The objective is to maximise the service level, which measures the probability of all jobs jointly completed before or at their due dates. For the problem, a new distributionally robust formulation is proposed, and two model-based approaches are developed: (1) a sample average approximation method is adapted, (2) a hierarchical approach based on mixed integer second-order cone programming (MI-SOCP) formulation is designed. To evaluate and compare the performance of the two approaches, randomly generated instances are tested. Computational results show that our proposed MI-SOCP-based hierarchical approach can obtain higher solution quality with less computational effect. [ABSTRACT FROM AUTHOR]

A recursive formula for computing the exact value of score vectors is proposed for a general form of the linear Gaussian state space model, which is more desirable than approximate values in some statistical analyses. Unlike most extant methods, our formula calculates all components of the score vector simultaneously. This approach significantly simplifies its programing, in particular, with some matrix-oriented programing languages, such as MATLAB. We also consider a way of handling initial conditions that depend on unknown parameters. This issue has not yet been explicitly addressed in the existing literature in the context of exact score computing for a general case, such as the one that we consider in this paper. It is also shown that our formula is especially useful for calculating score tests with an outer product of gradient asymptotic covariance matrix estimator. [ABSTRACT FROM AUTHOR]

Although the approach to correct for measurement errors in research has been known since the early 1970s, most researchers in the social sciences appear to ignore these recommendations. One possible reason is that the models with latent variables that were originally suggested may be too difficult to apply in practice. We suggest an alternative but simpler procedure to correct for measurement errors. If one knows the sizes of the random errors and method effects for the different measures, the correlation and covariance matrices for the observed variables can be corrected. This approach has already been shown for simple concepts measured by a single measure. In this paper, we show that this approach can be generalized to studies that use a mixture of simple and complex concepts measured by several questions. Using these corrected matrices as the basis for the estimation, the parameters of the models are automatically corrected for measurement errors. The conditions for the quality of these procedures will also be discussed. [ABSTRACT FROM AUTHOR]

The growing popularity of personalized medicine motivates people to explore individualized treatment regimes according to heterogeneous characteristics of the patients. For the large-scale data analysis, however, the data are collected at different times and different locations, i.e. subjects are usually from a heterogeneous population, which causes that the optimal treatment regimes also vary for patients across different subgroups. In this paper, we mainly focus on the estimation of optimal treatment regimes for subjects come from a heterogeneous population with high-dimensional data. We first remove the main effects of the covariates for each subgroup to eliminate non-ignorable residual confounding. Based on the centralized outcome, we propose a penalized robust learning that estimates the coefficient matrix of the interactions between covariates and treatment by penalizing pairwise differences of the coefficients of any two subgroups for the same covariate, which can automatically identify the latent complex structure of the coefficient matrix with heterogeneous and homogeneous columns. At the same time, the penalized robust learning can also select the important variables that truly contribute to the individualized treatment decisions with commonly used sparsity structure penalty. Extensive simulation studies show that our proposed method outperforms current popular methods, and it is further illustrated in the real analysis of the Tamoxifen breast cancer data. [ABSTRACT FROM AUTHOR]

There have been some advances in multivariate control charts in recent years. This paper presents a new simultaneous scheme for monitoring both the mean and variability of a multivariate normal process in a single chart, which is developed by improving and modifying another recently proposed scheme. We not only propose a new control scheme but also make it adaptive by varying all control chart parameters. Our scheme, for the first time, considers the process variability in two forms: "covariance matrix" and "multivariate coefficient of variation (MCV)". This scheme, again for the first time, considers simultaneous monitoring of the MCV with another process parameter (in our case, the mean vector). In addition, we develop a Markov chain model to compute the average run length and average time to signal values. We conduct extensive numerical analyses to measure the performance of the proposed scheme in two scenarios of process variability. At last, we present a numerical example by using a real dataset from a healthcare process to illustrate how the scheme can be implemented in practice. [ABSTRACT FROM AUTHOR]

In this paper, we propose approximations for the misclassification probabilities in linear discriminant analysis when the group means have a bilinear regression structure. First, we give a unified location and scale mixture expression of the standard normal distribution for the linear discriminant function. Then, the estimated approximations of misclassification are obtained for the three cases: unweighted case, weighted known covariance matrix Σ , and weighted unknown Σ. It has to be pointed out that larger p is better for classification when Σ is known, also in unweighted case. In the case Σ is unknown, we gain more information if fewer repeated measurements are used compared to when many repeated measurements closer to the number of included sample size are used. Furthermore, the accuracies of the proposed approximations are checked numerically by conducting a Monte Carlo simulation. [ABSTRACT FROM AUTHOR]

In a cluster randomized trial clusters of persons, for instance, schools or health centers, are assigned to treatments, and all persons in the same cluster get the same treatment. Although less powerful than individual randomization, cluster randomization is a good alternative if individual randomization is impossible or leads to severe treatment contamination (carry-over). Focusing on cluster randomized trials with a pretest and post-test of a quantitative outcome, this paper shows the equivalence of four methods of analysis: a three-level mixed (multilevel) regression for repeated measures with as levels cluster, person, and time, and allowing for unstructured between-cluster and within-cluster covariance matrices; a two-level mixed regression with as levels cluster and person, using change from baseline as outcome; a two-level mixed regression with as levels cluster and time, using cluster means as data; a one-level analysis of cluster means of change from baseline. Subsequently, similar equivalences are shown between a constrained mixed model and methods using the pretest as covariate. All methods are also compared on a cluster randomized trial on mental health in children. From these equivalences follows a simple method to calculate the sample size for a cluster randomized trial with baseline measurement, which is demonstrated step-by-step. [ABSTRACT FROM AUTHOR]

Multivariate repeated measures data naturally arise in clinical trials and other fields such as biomedical science, public health, agriculture, social science and so on. For data of this type, the classical approach is to conduct multivariate analysis of variance (MANOVA) based on Wilks' Lambda and other multivariate statistics, which require the assumptions of multivariate normality and homogeneity of within-cell covariance matrices. However, data being analyzed nowadays show marked departure from multivariate normality and homogeneity. This paper proposes a finite-sample test by modifying the sums of squares matrices to make them insensitive to the heterogeneity in MANOVA. The proposed test is invariant to affine transformation and robust against nonnormality. The proposed method can be used in various experimental designs, for example, factorial design and crossover design. Under various simulation settings, the proposed method outperforms the classical Doubly Multivariate Model and Multivariate Mixed Model proposed elsewhere, especially for unbalanced sample sizes with heteroscedasticity. The applications of the proposed method are illustrated with ophthalmology data in factorial and crossover designs. The proposed method successfully identified and validated a significant main effect and demonstrated that univariate analysis could be oversensitive to small but clinically unimportant interactions. [ABSTRACT FROM AUTHOR]

This paper introduces the K-combined vector random field, whose finite-dimensional characteristic functions are made up of certain power functions and whose finite-dimensional density functions are comprised of the modified Bessel functions of the second type. It is an elliptically contoured vector random field, contains K-differenced vector random field of Alsultan and Ma (2019) as a special case, and possesses all orders of moments. It is fully characterized by its mean vector function and its covariance matrix function, just like a Gaussian vector random field. With various selection of its parameters, its finite-dimensional distributions may have heavy tails or thin tails, comparing with a Gaussian one, and thus it provides a potential model for applications. We also investigate the usual stochastic ordering, the convex ordering, and the peakedness ordering of K-combined random fields and of multivariate K-combined distributions, with necessary and/or sufficient conditions derived. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the distributed recursive fault estimation problem for a class of discrete time-varying systems with binary encoding schemes over a sensor network. The fault signal with zero second-order difference is taken into account to reflect the sensor failures. Since the communication bandwidth in practice is constrained, the binary encoding schemes are exploited to regulate the signal transmission from the neighbouring sensors to the local fault estimator. In addition, due to the influence of channel noises, each bit might change with a small crossover probability. In the presence of sensor faults and bit errors, an upper bound for the estimation error covariance matrix is ensured and minimized at each time step via designing the gain matrices of the estimator. Finally, the effectiveness of the method is verified by a simulation. [ABSTRACT FROM AUTHOR]

Multivariate isotonic regression theory plays an important role in the field of testing statistical hypotheses under order restriction for several vector valued parameters and this problem may arise in several situations. Sasabuchi et al. derived a likelihood ratio type test for homogeneity of order restricted mean vectors under a multivariate normality assumption with unknown and common covariance matrices; however, its null distribution depends on the unknown covariance matrix. In order to overcome this difficulty, in the present paper we propose a test that conditions on the sufficient statistic for the covariance matrix. We remove the dependence of the null distribution of test statistic proposed by Sasabuchi et al. on the unknown value of covariance matrix and present a condition on a sufficient statistic for covariance matrix under the null hypothesis. A method based on Markov Chain Monte Carlo sampling is used to calculate the p - value of the test. We evaluate the operating characteristics of the proposed test through simulation studies. Our extensive simulation studies demonstrate that the power of this new test is generally higher than the test proposed by Sasabuchi et al. and also by Sasabuchi. A real data example is presented. [ABSTRACT FROM AUTHOR]

In this paper, we derive the exact finite sample distribution of the F ( = t 2 ) statistic for a single linear restriction on the regression parameters. We show that the F statistic can be expressed as a ratio of quadratic forms, and therefore its exact cumulative distribution under the null hypothesis can be derived from the result of Imhof [Computing the distribution of quadratic forms in normal variables. Biometrika. 1961;48(3/4):419–426]. A numerical calculation is carried out for the exact distribution of the F statistic using various HC covariance matrix estimators, and the rejection probability under the null hypothesis (size) based on the exact distribution is examined. The results show the exact finite sample distribution is remarkably reliable, while, in comparison, the use of the F-table leads to a serious over-rejection when the sample is not large or leveraged/unbalanced. [ABSTRACT FROM AUTHOR]

Estimating structured covariance or correlation matrix has been paid more and more attentions in recent years. A recent method based on the entropy loss function was proposed to regularize the covariance structure for a given covariance matrix whose underlying structure may be blurred due to random noises from different sources. However, the entropy loss function considered is very likely to be unavailable in covariance regularization for high-dimension and low-sample-size (HDLSS) data. In this paper, a new discrepancy is proposed for regularizing correlation structure, in which the given correlation matrix (e.g., sample correlation matrix) and the candidate structure in the entropy loss function are both added by the identity matrix multiplied by a constant, so that the problem owing to likely singularity of sample correlation matrix for HDLSS data can be overcome. The candidate correlation structures considered in this paper include tri-diagonal Toeplitz, compound symmetry, AR(1) and banded Toeplitz. The regularized correlation estimates for the first three structures can be obtained by solving one-dimensional optimization problems, while the regularized one for the fourth structure can be computed efficiently using Newton's iteration method. Simulation studies show that the proposed new approach works well, providing a reliable method to regularize the correlation structure for HDLSS data. [ABSTRACT FROM AUTHOR]