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Estimation of the mean vector and covariance matrix is of central importance in the analysis of multivariate data. In the framework of generalized linear models, usually the variances are certain functions of the means with the normal…

Methodology · Statistics 2023-01-25 Anupam Kundu , Mohsen Pourahmadi

In this article we derive an unbiased expression for the expected mean-squared error associated with continuously differentiable estimators of the noncentrality parameter of a chi-square random variable. We then consider the task of…

Applications · Statistics 2012-10-15 Florian Luisier , Thierry Blu , Patrick J. Wolfe

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…

Optimization and Control · Mathematics 2018-05-21 Viet Anh Nguyen , Daniel Kuhn , Peyman Mohajerin Esfahani

Consider a problem of predicting a response variable using a set of covariates in a linear regression model. If it is \emph{a priori} known or suspected that a subset of the covariates do not significantly contribute to the overall fit of…

Applications · Statistics 2011-09-13 SM Enayetur Raheem , S. Ejaz Ahmed

Shrinkage methods are frequently used to improve the precision of least squares estimators of fixed effects. However, widely used shrinkage estimators guarantee improved precision only under strong distributional assumptions. I develop an…

Econometrics · Economics 2025-09-09 Soonwoo Kwon

The exponential distribution is applied in a very wide variety of statistical procedures. Among the most prominent applications are those in the field of life testing and reliability theory. When there are two record samples available for…

Statistics Theory · Mathematics 2016-09-23 Hojatollah Zakerzadeh , Ali Akbar Jafari , Mahdieh Karimi

In this paper, we consider the problem of experience rating within the classic Markov chain life insurance framework. We begin by establishing a link between mixed Poisson distributions and the problem of pricing group disability insurance…

Statistics Theory · Mathematics 2025-11-14 Christian Furrer , Jacob Juhl Sørensen , Jorge Yslas

We propose a new class of estimators of the multivariate response linear regression coefficient matrix that exploits the assumption that the response and predictors have a joint multivariate Normal distribution. This allows us to indirectly…

Methodology · Statistics 2015-07-17 Aaron J. Molstad , Adam J. Rothman

We investigate Bayesian shrinkage methods for constructing predictive distributions. We consider the multivariate Normal model with a known covariance matrix and show that the Bayesian predictive density with respect to Stein's harmonic…

Statistics Theory · Mathematics 2017-07-31 Yuzo Maruyama , Toshio Ohnishi

We consider the question of learning the natural parameters of a $k$ parameter minimal exponential family from i.i.d. samples in a computationally and statistically efficient manner. We focus on the setting where the support as well as the…

Machine Learning · Computer Science 2021-11-01 Abhin Shah , Devavrat Shah , Gregory W. Wornell

This paper focuses on Bayesian shrinkage for covariance matrix estimation. We examine posterior properties and frequentist risks of Bayesian estimators based on new hierarchical inverse-Wishart priors. More precisely, we give the existence…

Methodology · Statistics 2011-06-17 Mathilde Bouriga , Olivier Féron

The James-Stein estimator is an estimator of the multivariate normal mean and dominates the maximum likelihood estimator (MLE) under squared error loss. The original work inspired great interest in developing shrinkage estimators for a…

Statistics Theory · Mathematics 2020-10-28 Chun-Hao Yang , Hani Doss , Baba C. Vemuri

In this paper we develop a very general class of bivariate discrete distributions. The basic idea is very simple. The marginals are obtained by taking the random geometric sum of a baseline distribution function. The proposed class of…

Methodology · Statistics 2018-05-22 Debasis Kundu

The assumption of normality in data has been considered in the field of statistical analysis for a long time. However, in many practical situations, this assumption is clearly unrealistic. It has recently been suggested that the use of…

Computation · Statistics 2016-11-25 Reinaldo B. Arellano-Valle , Javier E. Contreras-Reyes

The estimation of a multivariate mean $\theta$ is considered under natural modifications of balanced loss function of the form: (i) $\omega \, \rho(\|\delta-\delta_0\|^2) + (1-\omega) \, \rho(\|\delta-\theta\|^2) $, and (ii) $\ell \left(…

Statistics Theory · Mathematics 2019-04-08 Éric Marchand , William E. Strawderman

We compute asymptotic non-linear shrinkage formulas for covariance and precision matrix estimators for weighted sample covariances, and the joint sample-population eigenvector overlap distribution, in the spirit of Ledoit and P\'ech\'e. We…

Statistics Theory · Mathematics 2025-03-21 Benoit Oriol

In this paper, we introduce a class of improved estimators for the mean parameter matrix of a multivariate normal distribution with an unknown variance-covariance matrix. In particular, the main results of [D.Ch\'etelat and M. T.…

Statistics Theory · Mathematics 2024-06-25 Arash A. Foroushani , Severien Nkurunziza

We seek to improve estimates of the power spectrum covariance matrix from a limited number of simulations by employing a novel statistical technique known as shrinkage estimation. The shrinkage technique optimally combines an empirical…

Astrophysics · Physics 2009-11-13 Adrian C. Pope , István Szapudi

This paper considers the problem of estimating a high-dimensional (HD) covariance matrix when the sample size is smaller, or not much larger, than the dimensionality of the data, which could potentially be very large. We develop a…

Methodology · Statistics 2019-05-22 Esa Ollila , Elias Raninen

Modern datasets are trending towards ever higher dimension. In response, recent theoretical studies of covariance estimation often assume the proportional-growth asymptotic framework, where the sample size $n$ and dimension $p$ are…

Statistics Theory · Mathematics 2023-08-01 David L. Donoho , Michael J. Feldman