James-Stein estimators for the mean vector of a multivariate normal population based on independent samples from two normal populations with common covariance structure

The Stein phenomenon for monotone incomplete multivariate normal data

We establish the Stein phenomenon in the context of two-step, monotone incomplete data drawn from Np+q(μ,Σ), a (p+ q)-dimensional multivariate normal population with mean μ and covariance matrix Σ. On the basis of data consisting of n observations on all p+q characteristics and an additional N − n observations on the last q characteristics, where all observations are mutually independent, denot...

Estimation of the Multivariate Normal Mean under the Extended Reflected Normal Loss Function

Comparison of Small Area Estimation Methods for Estimating Unemployment Rate

Extended Abstract. In recent years, needs for small area estimations have been greatly increased for large surveys particularly household surveys in Sta­ tistical Centre of Iran (SCI), because of the costs and respondent burden. The lack of suitable auxiliary variables between two decennial housing and popula­ tion census is a challenge for SCI in using these methods. In general, the...

James-Stein type estimator by shrinkage to closed convex set with smooth boundary

We give James-Stein type estimators of multivariate normal mean vector by shrinkage to closed convex set K with smooth or piecewise smooth boundary. The rate of shrinkage is determined by the curvature of boundary of K at the projection point onto K . By considering a sequence of polytopes K j converging to K , we show that a particular estimator we propose is the limit of a sequence of estimat...

Characterization of Priors in the Stein Problem

The so-called Stein problem is addressed in the estimation of a mean vector of a multivariate normal distribution with a known covariance matrix. For general prior distributions with sphericity, the paper derives conditions on priors under which the resulting generalized Bayes estimators are minimax relative to the usual quadratic loss. It is also shown that the conditions can be expressed base...