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

Dan Zhuang (), S. Ejaz Ahmed (), Shuangzhe Liu () and Tiefeng Ma ()
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Dan Zhuang: Fujian Normal University
S. Ejaz Ahmed: Brock University
Shuangzhe Liu: University of Canberra
Tiefeng Ma: Southwestern University of Finance and Economics

Chapter Chapter 20 in Recent Developments in Multivariate and Random Matrix Analysis, 2020, pp 351-373 from Springer

Abstract: 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 ~ C C $$\tilde {\mu }_{CC}$$ 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.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-56773-6_20

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DOI: 10.1007/978-3-030-56773-6_20

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