Estimation of the Common Mean of Two Multivariate Normal Distributions Under Symmetrical and Asymmetrical Loss Functions

Dan Zhuang, S. Ejaz Ahmed, Shuangzhe Liu, Tiefeng Ma

Research output: A Conference proceeding or a Chapter in BookChapterpeer-review

Abstract

In this paper, the estimation of the common mean vector of two multivariate normal populations is considered and a new class of unbiased estimators is proposed. Several dominance results under the quadratic loss and LINEX loss functions are established. To illustrate the usefulness of these estimators, a simulation study with finite samples is conducted to compare them with four existing estimators, including the sample mean and the Graybill-Deal estimator. Based on the comparison studies, we found that the numerical performance of the proposed estimators is almost as good as μ~CC proposed by Chiou and Cohen (Ann Inst Stat Math 37:499–506, 1985) in terms of the risks. Its theoretical dominance over the sample mean of a single population under the sufficient conditions given is also established.
Original languageEnglish
Title of host publicationRecent Developments in Multivariate and Random Matrix Analysis
Subtitle of host publicationFestschrift in Honour of Dietrich von Rosen
EditorsThomas Holgersson, Martin Singull
Place of PublicationNetherlands
PublisherSpringer
Chapter20
Pages355-377
Number of pages23
ISBN (Electronic)9783030567736
ISBN (Print)9783030567729
DOIs
Publication statusPublished - 18 Sep 2020

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