Related papers: Estimation of mean vector in elliptical models

Shrinkage estimators have profound impacts in statistics and in scientific and engineering applications. In this article, we consider shrinkage estimation in the presence of linear predictors. We formulate two heteroscedastic hierarchical…

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…

We derive an optimal shrinkage sample covariance matrix (SCM) estimator which is suitable for high dimensional problems and when sampling from an unspecified elliptically symmetric distribution. Specifically, we derive the optimal (oracle)…

Let $X$ be a random vector with distribution $P_{\theta}$ where $\theta$ is an unknown parameter. When estimating $\theta$ by some estimator $\varphi(X)$ under a loss function $L(\theta,\varphi)$, classical decision theory advocates that…

This paper considers the regularized Tyler's scatter estimator for elliptical distributions, which has received considerable attention recently. Various types of shrinkage Tyler's estimators have been proposed in the literature and proved…

This review traces the evolution of theory that started when Charles Stein in 1955 [In Proc. 3rd Berkeley Sympos. Math. Statist. Probab. I (1956) 197--206, Univ. California Press] showed that using each separate sample mean from $k\ge3$…

Data in non-Euclidean spaces are commonly encountered in many fields of Science and Engineering. For instance, in Robotics, attitude sensors capture orientation which is an element of a Lie group. In the recent past, several researchers…

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…

In a linear regression model with random design, we consider a family of candidate models from which we want to select a `good' model for prediction out-of-sample. We fit the models using block shrinkage estimators, and we focus on the…

This paper focuses on investigating Stein's invariant shrinkage estimators for large sample covariance matrices and precision matrices in high-dimensional settings. We consider models that have nearly arbitrary population covariance…

This article studies two regularized robust estimators of scatter matrices proposed (and proved to be well defined) in parallel in (Chen et al., 2011) and (Pascal et al., 2013), based on Tyler's robust M-estimator (Tyler, 1987) and on…

This paper reviews advances in Stein-type shrinkage estimation for spherically symmetric distributions. Some emphasis is placed on developing intuition as to why shrinkage should work in location problems whether the underlying population…

In this paper, we propose the application of shrinkage strategies to estimate coefficients in the Bell regression models when prior information about the coefficients is available. The Bell regression models are well-suited for modeling…

We address high dimensional covariance estimation for elliptical distributed samples, which are also known as spherically invariant random vectors (SIRV) or compound-Gaussian processes. Specifically we consider shrinkage methods that are…

This paper is speculated to propose a class of shrinkage estimators for shape parameter beta in failure censored samples from two-parameter Weibull distribution when some 'apriori' or guessed interval containing the parameter beta is…

In the geosciences, a recurring problem is one of estimating spatial means of a physical field using weighted averages of point observations. An important variant is when individual observations are counted with some probability less than…

We tackle covariance estimation in low-sample scenarios, employing a structured covariance matrix with shrinkage methods. These involve convexly combining a low-bias/high-variance empirical estimate with a biased regularization estimator,…

Prediction of a vector of ordered parameters or part of it arises naturally in the context of Small Area Estimation (SAE). For example, one may want to estimate the parameters associated with the top ten areas, the best or worst area, or a…

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…

We develop a class of minimax estimators for a normal mean matrix under the Frobenius loss, which generalizes the James--Stein and Efron--Morris estimators. It shrinks the Schatten norm towards zero and works well for low-rank matrices. We…