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This article deal with the proposal of suggest and study of the properties of pre-test shrinkage estimators of Reliability Function for the Burr XII distribution using Progressive Type II censored sample. Since some difficulties to derive equations of risk function for proposed shrinkage estimators of reliability function under Precautionary Loss Function (PLF), we to study properties by using Monte-Carlo simulation. The numerical and Monte-Carlo simulations show that the performance of the proposed estimators is better than classical estimators in terms of relative risk. [ABSTRACT FROM AUTHOR]

Instead of applying the commonly used parametric Almon or Beta lag distribution of MIDAS, Breitung and Roling (J Forecast 34:588–603, 2015) suggested a nonparametric smoothed least-squares shrinkage estimator (henceforth SLS 1 ) for estimating mixed-frequency models. This SLS 1 approach ensures a flexible smooth trending lag distribution. However, even if the biasing parameter in SLS 1 solves the overparameterization problem, the cost is a decreased goodness-of-fit. Therefore, we suggest a modification of this shrinkage regression into a two-parameter smoothed least-squares estimator ( SLS 2 ). This estimator solves the overparameterization problem, and it has superior properties since it ensures that the orthogonality assumption between residuals and the predicted dependent variable holds, which leads to an increased goodness-of-fit. Our theoretical comparisons, supported by simulations, demonstrate that the increase in goodness-of-fit of the proposed two-parameter estimator also leads to a decrease in the mean square error of SLS 2 , compared to that of SLS 1 . Empirical results, where the inflation rate is forecasted based on the oil returns, demonstrate that our proposed SLS 2 estimator for mixed-frequency models provides better estimates in terms of decreased MSE and improved R2, which in turn leads to better forecasts. [ABSTRACT FROM AUTHOR]

In this article, a Stein-type weighted limited information maximum likelihood (LIML) estimator is proposed. It is based on a weighted average of the ordinary least squares (OLS) and LIML estimators, with weights inversely proportional to the Hausman test statistic. The asymptotic distribution of the proposed estimator is derived by means of local-to-exogenous asymptotic theory. In addition, the asymptotic risk of the Stein-type LIML estimator is calculated, and it is shown that the risk is strictly smaller than the risk of the LIML under certain conditions. A Monte Carlo simulation and an empirical application of a green patent dataset from Nordic countries are used to demonstrate the superiority of the Stein-type LIML estimator to the OLS, two-stage least squares, LIML and combined estimators when the number of instruments is large. [ABSTRACT FROM AUTHOR]

Summary: The binomial proportion is a classic parameter with many applications and has also been extensively studied in the literature. By contrast, the reciprocal of the binomial proportion, or the inverse proportion, is often overlooked, even though it also plays an important role in various fields. To estimate the inverse proportion, the maximum likelihood method fails to yield a valid estimate when there is no successful event in the Bernoulli trials. To overcome this zero‐event problem, several methods have been introduced in the previous literature. Yet to the best of our knowledge, there is little work on a theoretical comparison of the existing estimators. In this paper, we first review some commonly used estimators for the inverse proportion, study their asymptotic properties, and then develop a new estimator that aims to eliminate the estimation bias. We further conduct Monte Carlo simulations to compare the finite sample performance of the existing and new estimators, and also apply them to handle the zero‐event problem in a meta‐analysis of COVID‐19 data for assessing the relative risks of physical distancing on the infection of coronavirus. [ABSTRACT FROM AUTHOR]

In this study, a longitudinal regression model for covariance matrix outcomes is introduced. The proposal considers a multilevel generalized linear model for regressing covariance matrices on (time-varying) predictors. This model simultaneously identifies covariate-associated components from covariance matrices, estimates regression coefficients, and captures the within-subject variation in the covariance matrices. Optimal estimators are proposed for both low-dimensional and high-dimensional cases by maximizing the (approximated) hierarchical-likelihood function. These estimators are proved to be asymptotically consistent, where the proposed covariance matrix estimator is the most efficient under the low-dimensional case and achieves the uniformly minimum quadratic loss among all linear combinations of the identity matrix and the sample covariance matrix under the high-dimensional case. Through extensive simulation studies, the proposed approach achieves good performance in identifying the covariate-related components and estimating the model parameters. Applying to a longitudinal resting-state functional magnetic resonance imaging data set from the Alzheimer's Disease (AD) Neuroimaging Initiative, the proposed approach identifies brain networks that demonstrate the difference between males and females at different disease stages. The findings are in line with existing knowledge of AD and the method improves the statistical power over the analysis of cross-sectional data. [ABSTRACT FROM AUTHOR]

AbstractThe matrix-variate normal distribution is a probability distribution that is a generalization of the multivariate normal distribution to matrix-valued random variables. In this paper, we introduce a wavelet shrinkage estimator based on Stein’s unbiased risk estimate (SURE) threshold for matrix-variate normal distribution. We find a new SURE threshold for soft thresholding wavelet shrinkage estimator under the reflected normal balanced loss function in low and high dimensional cases. Also, we obtain the restricted wavelet shrinkage estimator based on non-negative sub matrix of the mean matrix. Finally, we present a simulation study to test the validity of the wavelet shrinkage estimator and two real examples for low and high dimensional data sets. [ABSTRACT FROM AUTHOR]

Shrinkage estimation in the gamma density using prior information is valuable in various fields, including finance, healthcare, and environmental science, where accurate parameter estimation is essential for decision-making and modeling. This manuscript considers the problem of estimation of θ α in Gamma density G(1/θ, p) when the prior estimate or guessed value of the parameter θ α is available in the form of point estimate θ 0 α . Some families of estimators of θ α are defined with its properties. Estimators developed by other authors are identified as particular members of the suggested families of shrinkage estimators. In particular, we have discussed the properties of the suggested families of estimators in an exponential distribution with known coefficient of variation. Numerical illustrations are also given in order to judge the merits of the proposed families of estimators over others. [ABSTRACT FROM AUTHOR]

Ridge regression is one of the most popular shrinkage estimation methods for linear models. Ridge regression effectively estimates regression coefficients in the presence of high-dimensional regressors. Recently, a generalized ridge estimator was suggested that involved generalizing the uniform shrinkage of ridge regression to non-uniform shrinkage; this was shown to perform well in sparse and high-dimensional linear models. In this paper, we introduce our newly developed R package "g.ridge" (first version published on 7 December 2023) that implements both the ridge estimator and generalized ridge estimator. The package is equipped with generalized cross-validation for the automatic estimation of shrinkage parameters. The package also includes a convenient tool for generating a design matrix. By simulations, we test the performance of the R package under sparse and high-dimensional settings with normal and skew-normal error distributions. From the simulation results, we conclude that the generalized ridge estimator is superior to the benchmark ridge estimator based on the R package "glmnet". Hence the generalized ridge estimator may be the most recommended estimator for sparse and high-dimensional models. We demonstrate the package using intracerebral hemorrhage data. [ABSTRACT FROM AUTHOR]

Semiparametric models hold promise to address many challenges to statistical inference that arise from real‐world applications, but their novelty and theoretical complexity create challenges for estimation. Taking advantage of the broad applicability of semiparametric models, we propose some novel and improved methods to estimate the regression coefficients of generalized partially linear models (GPLM). This model extends the generalized linear model by adding a nonparametric component. Like in parametric models, variable selection is important in the GPLM to single out the inactive covariates for the response. Instead of deleting inactive covariates, our approach uses them as auxiliary information in the estimation procedure. We then define two models, one that includes all the covariates and another that includes the active covariates only. We then combine these two model estimators optimally to form the pretest and shrinkage estimators. Asymptotic properties are studied to derive the asymptotic biases and risks of the proposed estimators. We show that if the shrinkage dimension exceeds two, the asymptotic risks of the shrinkage estimators are strictly less than those of the full model estimators. Extensive Monte Carlo simulation studies are conducted to examine the finite‐sample performance of the proposed estimation methods. We then apply our proposed methods to two real data sets. Our simulation and real data results show that the proposed estimators perform with higher accuracy and lower variability in the estimation of regression parameters for GPLM compared with competing estimation methods. [ABSTRACT FROM AUTHOR]

Confidence intervals are valuable tools in statistical practice for estimating binomial proportions, with the most well-known being the Wald and Clopper-Pearson intervals. However, it is known that these intervals perform poorly in terms of coverage probability and expected mean length, leading to the proposal of alternative intervals in the literature, although these may also have deficiencies. In this work, we investigate the performance of several of these confidence intervals using the parametric family p^c=X+cn+2c{\widehat{p}}_{c}=\frac{X+c}{n+2c} with c≥0c\ge 0 to estimate the parameter pp. Rather than using the confidence intervals approach, this analysis is done from the hypothesis tests approach. Our primary goal with this work is to identify values of cc that result in better-performing tests and to establish an optimal procedure.

The outcomes of many real-life experiments are sequences of record-breaking data sets, where only observations that exceed (or only those that fall below) the current extreme value are recorded. Records are needed when it is difficult to obtain observations or when observations are being destroyed when subjected to an experimental test. Records are applied in many real-life applications, such as hydrology, industrial stress testing, demise of glaciers, crop production, meteorological analysis, sporting and athletic events, and oil and mining surveys. For instance, in the threshold modeling the observations are those that cross a certain threshold value. Effectively estimating the location parameters for equally likely (uniformly distributed) records is needed in many real-life experiments. The practice demonstrated that the widely used estimators, such as the best linear unbiased estimator (BLUE) and maximum likelihood estimator (MLE), have some defects. This manuscript improves the MLE and BLUE of the location parameters for uniformly distributed records by investigating the corresponding shrinkage estimator using prior information about the BLUE and MLE. To measure the accuracy and precision of the proposed shrinkage estimator, the bias and mean square error (MSE) of the proposed estimators are investigated that provide sufficient conditions to get unbiased estimator with minimum MSE. The numerical results demonstrated that the proposed estimator are dominating over the existing estimators. [ABSTRACT FROM AUTHOR]

Marginal maximum likelihood estimation (MMLE) is commonly used for item response theory item parameter estimation. However, sufficiently large sample sizes are not always possible when studying rare populations. In this paper, empirical Bayes and hierarchical Bayes are presented as alternatives to MMLE in small sample sizes, using auxiliary item information to estimate the item parameters of a graded response model with higher accuracy. Empirical Bayes and hierarchical Bayes methods are compared with MMLE to determine under what conditions these Bayes methods can outperform MMLE, and to determine if hierarchical Bayes can act as an acceptable alternative to MMLE in conditions where MMLE is unable to converge. In addition, empirical Bayes and hierarchical Bayes methods are compared to show how hierarchical Bayes can result in estimates of posterior variance with greater accuracy than empirical Bayes by acknowledging the uncertainty of item parameter estimates. The proposed methods were evaluated via a simulation study. Simulation results showed that hierarchical Bayes methods can be acceptable alternatives to MMLE under various testing conditions, and we provide a guideline to indicate which methods would be recommended in different research situations. R functions are provided to implement these proposed methods. [ABSTRACT FROM AUTHOR]

This paper uses classical and shrinkage estimators to estimate the system reliability (R) in the stress-strength model when the stress and strength follow the Inverse Chen distribution (ICD). The comparisons of the proposed estimators have been presented using a simulation that depends on the mean squared error (MSE) criteria. [ABSTRACT FROM AUTHOR]

Abstract The estimation of mean vector parameters is very important in elliptical and spherically models. Among different methods, the Bayesian and shrinkage estimation are interesting. In this paper, the estimation of p-dimensional location parameter for p-variate elliptical and spherical distributions under an asymmetric loss function is investigated. We find generalized Bayes estimator of location parameters for elliptical and spherical distributions. Also we show the minimaxity and admissibility of generalized Bayes estimator in class of S S p ( θ , σ 2 I p ) . We introduce two new shrinkage soft-wavelet threshold estimators based on Huang shrinkage wavelet estimator (empirical) and Stein’s unbiased risk estimator (SURE) for elliptical and spherical distributions under non-linear exponential-balanced loss function. At the end, we present a simulation study to test the validity of the class of proposed estimators and physicochemical properties of the tertiary structure data set that is given to test the efficiency of this estimators in denoising. [ABSTRACT FROM AUTHOR]

In this paper, we suggested generalized shrinkage regression, ratio and regression-cumratio estimators for population mean in multi-phase stratified systematic (MPSS) sampling design using multi-auxiliary information when information on all auxiliary variables is not available for population. The expressions of mean square error and bias are derived for suggested estimators. The extension of these estimators in bivariate and multivariate is also discussed and some important special cases are deduced from the general class. An empirical and simulation studies are conducted to assess the performance of proposed design and estimators and found suggested MPSS design perform better than estimators of multi-phase simple random sampling estimators. [ABSTRACT FROM AUTHOR]

In this paper, we develop a penalized realized variance (PRV) estimator of the quadratic variation (QV) of a high-dimensional continuous Itô semimartingale. We adapt the principle idea of regularization from linear regression to covariance estimation in a continuous-time high-frequency setting. We show that under a nuclear norm penalization, the PRV is computed by soft-thresholding the eigenvalues of realized variance (RV). It therefore encourages sparsity of singular values or, equivalently, low rank of the solution. We prove our estimator is minimax optimal up to a logarithmic factor. We derive a concentration inequality, which reveals that the rank of PRV is—with a high probability—the number of non-negligible eigenvalues of the QV. Moreover, we also provide the associated non-asymptotic analysis for the spot variance. We suggest an intuitive data-driven subsampling procedure to select the shrinkage parameter. Our theory is supplemented by a simulation study and an empirical application. The PRV detects about three–five factors in the equity market, with a notable rank decrease during times of distress in financial markets. This is consistent with most standard asset pricing models, where a limited amount of systematic factors driving the cross-section of stock returns are perturbed by idiosyncratic errors, rendering the QV—and also RV—of full rank. [ABSTRACT FROM AUTHOR]

The Gamma Regression Model (GRM) has a variety of applications in medical sciences and other disciplines. The results of the GRM may be misleading in the presence of multicollinearity. In this article, a new biased estimator called James-Stein estimator is proposed to reduce the impact of correlated regressors for the GRM. The mean squared error (MSE) properties of the proposed estimator are derived and compared with the existing estimators. We conducted a simulation study and employed the MSE and bias evaluation criterion to judge the proposed estimator's performance. Finally, two medical dataset are considered to show the benefit of the proposed estimator over existing estimators. [ABSTRACT FROM AUTHOR]

The reliability of the stress-strength model attracted many statisticians for several years owing to its applicability in different and diverse parts such as engineering, quality control, and economics. In this paper, the system reliability estimation in the stress-strength model containing Kth parallel components will be offered by four types of shrinkage methods: constant Shrinkage Estimation Method, Shrinkage Function Estimator, Modified Thompson Type Shrinkage Estimator, Squared Shrinkage Estimator. The Monte Carlo simulation study is compared among proposed estimators using the mean squared error. The result analyses of the shrinkage estimation methods showed that the shrinkage functions estimator was the best since it has a minor mean squared error than the other methods followed by the additional shrinkage estimator. The stress and strength belong to the In verse Kumaraswamy distribution

The problem of estimating the mean of a multivariate normal distribution by different types of shrinkage estimators is investigated. Under the balanced loss function, we establish the minimaxity of the James-Stein estimator. When the dimension of the parameters space and the sample size tend to infinity, we study the asymptotic behavior of risks ratio of James-Stein estimator to the maximum likelihood estimator. The positive-part of James-Stein estimator is also treated. [ABSTRACT FROM AUTHOR]

In the paper we consider a new approach to regularize the maximum likelihood estimator of a discrete probability distribution and its application in variable selection. The method relies on choosing a parameter of its convex combination with a low-dimensional target distribution by minimising the squared error (SE) instead of the mean SE (MSE). The choice of an optimal parameter for every sample results in not larger MSE than MSE for James–Stein shrinkage estimator of discrete probability distribution. The introduced parameter is estimated by cross-validation and is shown to perform promisingly for synthetic dependence models. The method is applied to introduce regularized versions of information based variable selection criteria which are investigated in numerical experiments and turn out to work better than commonly used plug-in estimators under several scenarios. [ABSTRACT FROM AUTHOR]

We addressed the problem of estimating regression coefficients for partially linear models, where the nonparametric component is approximated using smoothing splines and subspace information is available. We proposed pretest and shrinkage estimation strategies using the profile likelihood estimator as the benchmark. We examined the asymptotic distributional bias and risk of the proposed estimators, and assessed their relative performance with respect to the unrestricted profile likelihood estimator under varying degrees of uncertainty in the subspace information. The shrinkage-based estimators uniformly dominated the unrestricted profile likelihood estimator. The positive-part shrinkage estimator was shown to be more efficient than the others, and was robust against uncertain subspace information. We also compared the performance of penalty estimators with those of the proposed estimators via a Monte Carlo simulation, and found that the proposed estimators were more efficient. The proposed estimation strategies were applied to a real dataset to evaluate their practical usefulness. The results were consistent with those from theory and simulation. [ABSTRACT FROM AUTHOR]

Unbiased estimators of the population parameters are often used to make an inference about the population. In cases where unbiased estimators have large variance, biased estimators such as shrinkage estimators may be preferred. In this study, shrinkage estimators of the location parameter of the normal distribution were obtained under ranked set sampling and median ranked set sampling. In addition, mean square errors of shrinkage estimators were obtained theoretically under ranked set sampling and median ranked set sampling. In order to examine the efficiency of the estimators, the mean square errors were calculated under different conditions using Monte Carlo simulation study. According to the results, it was observed that the shrinkage estimators obtained under median ranked set sampling were more efficient than the shrinkage estimators obtained under ranked set sampling and simple random sampling. [ABSTRACT FROM AUTHOR]

In this paper, we studied estimators based on an interval shrinkage with equal weights point shrinkage estimators for all individual target points ¯θ ∈ (θ0,θ1) for exponentially distributed observations in the presence of outliers drawn from a uniform distribution. Estimators obtained from both shrinkage and interval shrinkage were compared, showing that the estimators obtained via the interval shrinkage method perform better. Symmetric and asymmetric loss functions were also used to calculate the estimators. Finally, a numerical study and illustrative examples were provided to describe the results. [ABSTRACT FROM AUTHOR]

This study is concerned with the problem of estimating the reliability function of the parameters of the two-parameter Burr XII distribution when the data are complete. Concepts such as the likelihood estimator, bias, bias ratio, and mean square error are defined. The purpose of this research is investigate the properties of the double-stage shrinkage estimators (DSSEs) of the reliability function of Burr XII distribution and obtain the equations of bias, mean square error, and bias ratio. The relative efficiency of the Burr XII distribution of the proposed estimators is also investigated by deriving their equations. Numerical results show performance of our estimators to be better than those of the classical pooled estimators based on the relative efficiency criteria. In particular, our proposed DSSEs have better performance than the classical estimator and single-stage shrinkage estimators.

The paper considers the problem of estimation of the regression coefficients in a Poisson regression model under multicollinearity situation. We propose non-penalty Stein-type shrinkage ridge estimation approach when it is conjectured that some prior information is available in the form of potential linear restrictions on the coefficients. We establish the asymptotic distributional biases and risks of the proposed estimators and investigate their relative performance with respect to the unrestricted ridge estimator. For comparison sake, we consider the two penalty estimators, namely, least absolute shrinkage and selection operator and Elastic-Net estimators and compare numerically their relative performance with the other listed estimators. Monte-Carlo simulation experiment is conducted to evaluate the performance of each estimator in terms of the simulated relative efficiency. The results show that the shrinkage ridge estimators perform better than the penalty estimators in certain parts of the parameter space. Finally, a real data example is illustrated to evaluate of the proposed methods. [ABSTRACT FROM AUTHOR]

In this article, we propose a shrinkage estimator for the scale parameter of the Gamma distribution when the prior information is available and compare it with minimum mean square error (MMSE) of its usual estimator in the sense of efficiency. The proposed shrinkage estimator has smaller Mean Square Error (MSE) than MMSE estimator when the prior estimate is good. The properties of shrinkage estimator have been studied in terms of bias and mean square error. Numerical illustrations are carried out to throw light on the performance of the proposed method of estimation other conventional estimators. [ABSTRACT FROM AUTHOR]

The least squares estimator (LSE) seems a natural estimator of linear regression models. Whereas, if the dimension of the vector of regression coefficients is greater than 1 and the residuals are dependent, the best linear unbiased estimator (BLUE), which includes the information of the covariance matrix Γ of residual process has a better performance than LSE in the sense of mean square error. As we know the unbiased estimators are generally inadmissible, Senda and Taniguchi (2006) introduced a James–Stein type shrinkage estimator for the regression coefficients based on LSE, where the residual process is a Gaussian stationary process, and provides sufficient conditions such that the James–Stein type shrinkage estimator improves LSE. In this paper, we propose a shrinkage estimator based on BLUE. Sufficient conditions for this shrinkage estimator to improve BLUE are also given. Furthermore, since Γ is infeasible, assuming that Γ has a form of Γ = Γ (θ) , we introduce a feasible version of that shrinkage estimator with replacing Γ (θ) by Γ (θ ˆ) which is introduced in Toyooka (1986). Additionally, we give the sufficient conditions where the feasible version improves BLUE. Besides, the results of a numerical studies confirm our approach. [ABSTRACT FROM AUTHOR]

Previous efforts in gene network reconstruction have mainly focused on data-driven modeling, with little attention paid to knowledge-based approaches. Leveraging prior knowledge, however, is a promising paradigm that has been gaining momentum in network reconstruction and computational biology research communities. This paper proposes two new algorithms for reconstructing a gene network from expression profiles with and without prior knowledge in small sample and high-dimensional settings. First, using tools from the statistical estimation theory, particularly the empirical Bayesian approach, the current research estimates a covariance matrix via the shrinkage method. Second, estimated covariance matrix is employed in the penalized normal likelihood method to select the Gaussian graphical model. This formulation allows the application of prior knowledge in the covariance estimation, as well as in the Gaussian graphical model selection. Experimental results on simulated and real datasets show that, compared to state-of-the-art methods, the proposed algorithms achieve better results in terms of both PR and ROC curves. Finally, the present work applies its method on the RNA-seq data of human gastric atrophy patients, which was obtained from the EMBL-EBI database. The source codes and relevant data can be downloaded from: https://github.com/AbbaszadehO/DKGN. [ABSTRACT FROM AUTHOR]

In this paper, we consider two forms of shrinkage estimators of the mean θ of a multivariate normal distribution X ~ Np(θ, σ²Ip) in Rp where σ² is unknown and estimated by the statistic S² (S² ~ σ²?²n). Estimators that shrink the components of the usual estimator X to zero and estimators of Lindley-type, that shrink the components of the usual estimator to the random variable X̄. Our aim is to improve under appropriate condition the results related to risks ratios of shrinkage estimators, when n and p tend to infinity and to ameliorate the results of minimaxity obtained previously of estimators cited above, when the dimension p is finite. Some numerical results are also provided. [ABSTRACT FROM AUTHOR]

Pareto distributions are useful for modeling the loss data in many fields such as actuarial science, economics, insurance, hydrology and reliability theory. In this paper, we consider the simultaneous estimation of the risk parameters of Pareto distributions from the perspective of empirical Bayes, novel SURE-type shrinkage estimators are developed by employing the Stein's unbiased estimate of risk (SURE). Specifically, due to the lacking of the analytic form for the risk function, we propose to estimate the hyperparameters by minimizing an unbiased estimate of an approximation of the risk function. Under mild conditions, we prove the optimality of the new shrinkage estimators. The performance of our estimators is illustrated with simulation studies and an analysis of a real auto insurance claim dataset. [ABSTRACT FROM AUTHOR]

The central focus of this paper is upon the alleviation of the boundary problem when the probability density function has a bounded support. Mixtures of beta densities have led to different methods of density estimation for data assumed to have compact support. Among these methods, we mention Bernstein polynomials which leads to an improvement of edge properties for the density function estimator. In this paper, we set forward a shrinkage method using the Bernstein polynomial and a finite Gaussian mixture model to construct a semi-parametric density estimator, which improves the approximation at the edges. Some asymptotic properties of the proposed approach are investigated, such as its probability convergence and its asymptotic normality. In order to evaluate the performance of the proposed estimator, a simulation study and some real data sets were carried out. [ABSTRACT FROM AUTHOR]

Note. The best result in each experiment is highlighted in bold.The optimal solutions of many decision problems such as the Markowitz portfolio allocation and the linear discriminant analysis depend on the inverse covariance matrix of a Gaussian random vector. In "Distributionally Robust Inverse Covariance Estimation: The Wasserstein Shrinkage Estimator," Nguyen, Kuhn, and Mohajerin Esfahani propose a distributionally robust inverse covariance estimator, obtained by robustifying the Gaussian maximum likelihood problem with a Wasserstein ambiguity set. In the absence of any prior structural information, the estimation problem has an analytical solution that is naturally interpreted as a nonlinear shrinkage estimator. Besides being invertible and well conditioned, the new shrinkage estimator is rotation equivariant and preserves the order of the eigenvalues of the sample covariance matrix. If there are sparsity constraints, which are typically encountered in Gaussian graphical models, the estimation problem can be solved using a sequential quadratic approximation algorithm. We introduce a distributionally robust maximum likelihood estimation model with a Wasserstein ambiguity set to infer the inverse covariance matrix of a p-dimensional Gaussian random vector from n independent samples. The proposed model minimizes the worst case (maximum) of Stein's loss across all normal reference distributions within a prescribed Wasserstein distance from the normal distribution characterized by the sample mean and the sample covariance matrix. We prove that this estimation problem is equivalent to a semidefinite program that is tractable in theory but beyond the reach of general-purpose solvers for practically relevant problem dimensions p. In the absence of any prior structural information, the estimation problem has an analytical solution that is naturally interpreted as a nonlinear shrinkage estimator. Besides being invertible and well conditioned even for p>n , the new shrinkage estimator is rotation equivariant and preserves the order of the eigenvalues of the sample covariance matrix. These desirable properties are not imposed ad hoc but emerge naturally from the underlying distributionally robust optimization model. Finally, we develop a sequential quadratic approximation algorithm for efficiently solving the general estimation problem subject to conditional independence constraints typically encountered in Gaussian graphical models. [ABSTRACT FROM AUTHOR]

Clustering is an important task in statistics and many other scientific fields. In this note, we propose an improved K-means clustering approach called 'enhanced shrinkage K-means' based on the James-Stein estimator and learning vector quantization (LVQ) algorithm. The basic idea of this new algorithm is taking into account of the strength of both unsupervised clustering and supervised classification methods, in which we shrink the clustering centers toward the prototype vector via James-Stein estimator. We carry out extensive simulation studies and real data analysis to evaluate the performance of this new approach, and obtain encouraging results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new shrinkage soft-wavelet threshold estimator based on Stein's unbiased risk estimate (SURE) for elliptical and spherical distributions under balanced loss functions. we focus on particular thresholding rules to obtain a new threshold, and thus produce new estimators. In addition, we obtain SURE shrinkage based on nonnegative subset of the mean vector. Finally, we present a simulation to test the validity of the proposed estimator. [ABSTRACT FROM AUTHOR]

The preliminary test shrinkage estimator for estimating the mean (α) of normal distribution was presented in this article when a prior guess (α0) of the actual (α) on hand using shrinkage weight factor Ψ(·) in addition to pretest region (R). Equations for Bias, Mean Squared Error and Relative Efficiency for the recommended estimator were resulting. Statistical outcome and discussions were drawn about collection different (constant) including in previous equations. Comparisons between optional estimator with usual and some existing works were given based on Bias and relative efficiency. Finally, the conclusions in this context are displayed. [ABSTRACT FROM AUTHOR]

In this paper, the problem of estimating the mean vector under non-negative constraints on location vector of the multivariate normal distribution is investigated. The value of the wavelet threshold based on Stein's unbiased risk estimators is calculated for the shrinkage estimator in restricted parameter space. We suppose that covariance matrix is unknown and we find the dominant class of shrinkage estimators under Balance loss function. The performance evaluation of the proposed class of estimators is checked through a simulation study by using risk and average mean square error values. [ABSTRACT FROM AUTHOR]

In this article, we propose Liu-type shrinkage estimators for the zero-inflated Poisson regression (ZIPR) model in the presence of multicollinearity. Our new approach is a remedy to the problem of inflated variances for the ML estimation technique—which is a standard approach to estimate these types of count data models. When the data are in the form of non-negative integers with a surplus of zeros it induces overdispersion in the dependent variable. Considerable multicollinearity is frequently observed, but usually disregarded, for these types of data sets. Based on a Monte Carlo study we illustrate that our proposed estimators exhibit better MSE and MAE than the usual ML estimator and some other Liu estimators in the presence of multicollinearity. To demonstrate the advantages and the empirical relevance of our improved estimators, maternal death data are analyzed and the results illustrate similar benefits as is demonstrated in our simulation study. [ABSTRACT FROM AUTHOR]

The Internet of things ((IoT) consisted of physical devices networks such as sensors, home appliances, electronics, and software’s. It enables us to collect and exchange data in several fields. After data collection from IoT, variable selection is considered a major problem because many variables are involved in real life datasets. The current study focused on large data analysis of the problem of model selection, including interaction terms. The dataset used in this study is taken from solar drier with moisture ratio removal (%) as dependent variable while ambient temperature, chamber temperature, collector temperature, chamber relative humidity, ambient relative humidity, and solar radiation as independent variables. LASSO with Huber M, LASSO with Hampel M and LASSO with Bisquare M are used in this study. Comparison of techniques are made with ridge regression and OLS (ordinary least square) after multicollinearity test and coefficient test. MAPE (mean absolute percentage error) for the efficient selected model is used to forecast with its minimum possible value. As a result, the hybrid model of LASSO with Bisquare-M is considered as the efficient model with its minimum MAPE value. Thus, the resulting model with the selected variables can be used to predict Moisture Ratio Removal (%) to determine seaweed drying behavior. [ABSTRACT FROM AUTHOR]

Introduction: In recent years, brain functional connectivity studies are extended using the advanced statistical methods. Functional connectivity is identified by synchronous activation in a spatially distinct region of the brain in resting-state functional Magnetic Resonance Imaging (MRI) data. For this purpose there are several methods such as seed-based correlation analysis based on temporal correlation between different Regions of Interests (ROIs) or between brain’s voxels of prior seed. Methods: In the current study, test-retest Resting State functional MRI (rs-fMRI) data of 21 healthy subjects were analyzed to predict second replication connectivity map using first replication data. A potential estimator is “raw estimator” that uses the first replication data from each subject to predict the second replication connectivity map of the same subject. The second estimator, “mean estimator” uses the average of all sample subjects' connectivity to estimate the correlation map. Shrinkage estimator is made by shrinking raw estimator towards the average connectivity map of all subjects' first replicate. Prediction performance of the second replication correlation map is evaluated by Mean Squared Error (MSE) criteria. Results: By the employment of seed-based correlation analysis and choosing precentral gyrus as the ROI over 21 subjects in the study, on average MSE for raw, mean and shrinkage estimator were 0.2169, 0.1118, and 0.1103, respectively. Also, percent reduction of MSE for shrinkage and mean estimator in comparison with raw estimator is 49.14 and 48.45, respectively. Conclusion: Shrinkage approach has the positive effect on the prediction of functional connectivity. When data has a large between session variability, prediction of connectivity map can be improved by shrinking towards population mean.

Abstract Parameter estimation in multivariate analysis is important, particularly when parameter space is restricted. Among different methods, the shrinkage estimation is of interest. In this article we consider the problem of estimating the p-dimensional mean vector in spherically symmetric models. A dominant class of Baranchik-type shrinkage estimators is developed that outperforms the natural estimator under the balance loss function, when the mean vector is restricted to lie in a non-negative hyperplane. In our study, the components of the diagonal covariance matrix are assumed to be unknown. The performance evaluation of the proposed class of estimators is checked through a simulation study along with a real data analysis.

Recently it has been shown that when Principal Component Analysis is applied as a dictionary learning technique to Compressive Sensing-based data aggregation, using a Deterministic Node Selection method for data collection in Wireless Sensor Networks can outperform Random Node Selection ones. In this paper, a new scheduling method for selection of measured nodes in a data collection round, called "Information-Based Deterministic Node Selection", is proposed. Simulation results for synthetic and real data sets show that the proposed method outperforms a reference DNS method in terms of energy consumption per reconstruction error. Correlation (or covariance) matrix estimation is necessary for DNS strategies which are accomplished by gathering data from all network nodes in a few initial time slots of collection rounds. In this regard, we also propose the use of a particular type of shrinkage estimator in preference to the standard correlation matrix estimator. With the aid of the new estimator, we can obtain data correlations with the same accuracy of standard estimator while we need less number of observations. Our numerical experiments demonstrate that when the number of measured nodes is less than 50% of the total nodes, using shrinkage estimator causes extra energy savings in sensor nodes. [ABSTRACT FROM AUTHOR]

To estimate the treatment effect in an observational study, we use a semiparametric locally efficient dimension-reduction approach to assess the treatment assignment mechanisms and average responses in both the treated and the nontreated groups. We then integrate our results using imputation, inverse probability weighting, and doubly robust augmentation estimators. Doubly robust estimators are locally efficient, and imputation estimators are super-efficient when the response models are correct. To take advantage of both procedures, we introduce a shrinkage estimator that combines the two. The proposed estimators retains the double robustness property, while improving on the variance when the response model is correct. We demonstrate the performance of these estimators using simulated experiments and a real data set on the effect of maternal smoking on baby birth weight. [ABSTRACT FROM AUTHOR]