Related papers: Improved robust Bayes estimators of the error vari…

Estimation of the ordered scale parameter of a two scale mixture of the exponential distribution is considered under Stein loss and symmetric loss. Under certain conditions, we prove that the inadmissibility equivariant estimator exhibits…

The Bayes linear estimator is derived by minimizing the Bayes risk with respect to the squared loss function. Non-unbiased estimators such as ordinary ridge, typical shrinkage, fractional rank, and restricted least squares estimators, as…

We derive minimax generalized Bayes estimators of regression coefficients in the general linear model with spherically symmetric errors under invariant quadratic loss for the case of unknown scale. The class of estimators generalizes the…

This paper concerns the robust regression model when the number of predictors and the number of observations grow in a similar rate. Theory for M-estimators in this regime has been recently developed by several authors [El Karoui et al.,…

For normal canonical models, and more generally a vast array of general spherically symmetric location-scale models with a residual vector, we consider estimating the (univariate) location parameter when it is lower bounded. We provide…

We study admissibility of a subclass of generalized Bayes estimators of a multivariate normal vector when the variance is unknown, under scaled quadratic loss. Minimaxity is also established for certain of these estimators.

We give a sufficient condition for admissibility of generalized Bayes estimators of the location vector of spherically symmetric distribution under squared error loss. Compared to the known results for the multivariate normal case, our…

This study investigates component wise estimation of ordered variances of scale mixture of two normal distributions. For this study two special loss functions are considered namely squared error loss function and entropy loss function. We…

In this paper we propose a new Bayesian estimation method to solve linear inverse problems in signal and image restoration and reconstruction problems which has the property to be scale invariant. In general, Bayesian estimators are {\em…

In this paper we analyze, for a model of linear regression with gaussian covariates, the performance of a Bayesian estimator given by the mean of a log-concave posterior distribution with gaussian prior, in the high-dimensional limit where…

In the estimation of the mean matrix in a multivariate normal distribution, the generalized Bayes estimators with closed forms are provided, and the sufficient conditions for their minimaxity are derived relative to both matrix and scalar…

Let y=A\beta+\epsilon, where y is an N\times1 vector of observations, \beta is a p\times1 vector of unknown regression coefficients, A is an N\times p design matrix and \epsilon is a spherically symmetric error term with unknown scale…

The problem of reducing the bias of maximum likelihood estimator in a general multivariate elliptical regression model is considered. The model is very flexible and allows the mean vector and the dispersion matrix to have parameters in…

Assuming an exponential power distribution is one way to deal with outliers in regression and clustering, which can increase the robustness of the analysis. Gaussian distribution is a special case of an exponential distribution. And an…

We consider the problem of linear fitting of noisy data in the case of broad (say $\alpha$-stable) distributions of random impacts ("noise"), which can lack even the first moment. This situation, common in statistical physics of small…

The problem of estimating a normal covariance matrix is considered from a decision-theoretic point of view, where the dimension of the covariance matrix is larger than the sample size. This paper addresses not only the nonsingular case but…

In this paper, we consider the multicollinearity problem in the gamma regression model when model parameters are linearly restricted. The linear restrictions are available from prior information to ensure the validity of scientific theories…

Consider the Gaussian sequence model under the additional assumption that a fixed fraction of the means is known. We study the problem of variance estimation from a frequentist Bayesian perspective. The maximum likelihood estimator (MLE)…

Multivariate Bayesian error-in-variable (EIV) linear regression is considered to account for additional additive Gaussian error in the features and response. A 3-variable deterministic scan Gibbs samplers is constructed for multivariate EIV…

We analyze the connection between minimizers with good generalizing properties and high local entropy regions of a threshold-linear classifier in Gaussian mixtures with the mean squared error loss function. We show that there exist…