Related papers: Ensemble minimaxity of James-Stein estimators

Consider the problem of estimating a multivariate normal mean with a known variance matrix, which is not necessarily proportional to the identity matrix. The coordinates are shrunk directly in proportion to their variances in Efron and…

In this work, the estimation of the multivariate normal mean by different classes of shrinkage estimators is investigated. The risk associated with the balanced loss function is used to compare two estimators. We start by considering…

Towards understanding the fundamental limits of estimation from data of varied quality, we study the problem of estimating a mean parameter from heteroskedastic Gaussian observations where the variances are unknown and may vary arbitrarily…

We present the first minimax risk bounds for estimators of the spectral measure in multivariate linear factor models, where observations are linear combinations of regularly varying latent factors. Non-asymptotic convergence rates are…

In this paper, we consider the estimation of a mean vector of a multivariate normal population where the mean vector is suspected to be nearly equal to mean vectors of $k-1$ other populations. As an alternative to the preliminary test…

A new class of minimax Stein-type shrinkage estimators of a multivariate normal mean is studied where the shrinkage factor is based on an l_p norm. The proposed estimators allow some but not all coordinates to be estimated by 0 thereby…

Inference about dependencies in a multiway data array can be made using the array normal model, which corresponds to the class of multivariate normal distributions with separable covariance matrices. Maximum likelihood and Bayesian methods…

Many statistical practices involve choosing between a full model and reduced models where some coefficients are reduced to zero. Data were used to select a model with estimated coefficients. Is it possible to do so and still come up with an…

The problem of estimating the mean of a normal vector with known but unequal variances introduces substantial difficulties that impair the adequacy of traditional empirical Bayes estimators. By taking a different approach, that treats the…

Shrinkage estimation usually reduces variance at the cost of bias. But when we care only about some parameters of a model, I show that we can reduce variance without incurring bias if we have additional information about the distribution of…

The James-Stein estimator has attracted much interest as a shrinkage estimator that yields better estimates than the maximum likelihood estimator. The James-Stein estimator is also very useful as an argument in favor of empirical Bayesian…

The James-Stein estimator is a biased estimator -- for a finite number of samples its expected value is not the true mean. The maximum-likelihood estimator (MLE), is unbiased and asymptotically optimal. Yet, when estimating the mean of $3$…

We consider estimation of a multivariate normal mean vector under sum of squared error loss. We propose a new class of smooth estimators parameterized by \alpha dominating the James-Stein estimator. The estimator for \alpha=1 corresponds to…

This paper is a follow-up to Maruyama and Strawderman (2006, Journal of Statistical Planning and Inference), which identified a new class of generalized Bayes estimators with a particularly simple form for estimating a normal variance under…

This paper presents a novel approach to constructing estimators that dominate the classical James-Stein estimator under the quadratic loss for multivariate normal means. Building on Stein's risk representation, we introduce a new sufficient…

Analytic evaluation of heteroskedasticity consistent covariance matrix estimates (HCCME) is difficult because of the complexity of the formulae currently available. We obtain new analytic formulae for the bias of a class of estimators of…

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…

The estimation of the mean matrix of the multivariate normal distribution is addressed in the high dimensional setting. Efron-Morris-type linear shrinkage estimators based on ridge estimators for the precision matrix instead of the…

The nested error regression model is a useful tool for analyzing clustered (grouped) data, and is especially used in small area estimation. The classical nested error regression model assumes normality of random effects and error terms, and…

In many statistical problems, stochastic signals can be represented as a sequence of noisy wavelet coefficients. In this paper, we develop general empirical Bayes methods for the estimation of true signal. Our estimators approximate certain…