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

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

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

Information Systems

Research output: A Conference proceeding or a Chapter in Book › Chapter › peer-review

2 Citations (Scopus)

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 language	English
Title of host publication	Recent Developments in Multivariate and Random Matrix Analysis
Subtitle of host publication	Festschrift in Honour of Dietrich von Rosen
Editors	Thomas Holgersson, Martin Singull
Place of Publication	Netherlands
Publisher	Springer
Chapter	20
Pages	351-373
Number of pages	23
ISBN (Electronic)	9783030567736
ISBN (Print)	9783030567729
DOIs	https://doi.org/10.1007/978-3-030-56773-6_20 https://doi.org/10.1007/978-3-030-56773-6_20
Publication status	Published - 18 Sept 2020

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Zhuang, D., Ahmed, S. E., Liu, S., & Ma, T. (2020). Estimation of the Common Mean of Two Multivariate Normal Distributions Under Symmetrical and Asymmetrical Loss Functions. In T. Holgersson, & M. Singull (Eds.), Recent Developments in Multivariate and Random Matrix Analysis: Festschrift in Honour of Dietrich von Rosen (pp. 351-373). Springer. https://doi.org/10.1007/978-3-030-56773-6_20, https://doi.org/10.1007/978-3-030-56773-6_20

Zhuang, Dan ; Ahmed, S. Ejaz ; Liu, Shuangzhe et al. / Estimation of the Common Mean of Two Multivariate Normal Distributions Under Symmetrical and Asymmetrical Loss Functions. Recent Developments in Multivariate and Random Matrix Analysis: Festschrift in Honour of Dietrich von Rosen. editor / Thomas Holgersson ; Martin Singull. Netherlands : Springer, 2020. pp. 351-373

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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.",

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Zhuang, D, Ahmed, SE, Liu, S & Ma, T 2020, Estimation of the Common Mean of Two Multivariate Normal Distributions Under Symmetrical and Asymmetrical Loss Functions. in T Holgersson & M Singull (eds), Recent Developments in Multivariate and Random Matrix Analysis: Festschrift in Honour of Dietrich von Rosen. Springer, Netherlands, pp. 351-373. https://doi.org/10.1007/978-3-030-56773-6_20, https://doi.org/10.1007/978-3-030-56773-6_20

Estimation of the Common Mean of Two Multivariate Normal Distributions Under Symmetrical and Asymmetrical Loss Functions. / Zhuang, Dan; Ahmed, S. Ejaz; Liu, Shuangzhe et al.
Recent Developments in Multivariate and Random Matrix Analysis: Festschrift in Honour of Dietrich von Rosen. ed. / Thomas Holgersson; Martin Singull. Netherlands: Springer, 2020. p. 351-373.

Research output: A Conference proceeding or a Chapter in Book › Chapter › peer-review

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Zhuang D, Ahmed SE, Liu S, Ma T. Estimation of the Common Mean of Two Multivariate Normal Distributions Under Symmetrical and Asymmetrical Loss Functions. In Holgersson T, Singull M, editors, Recent Developments in Multivariate and Random Matrix Analysis: Festschrift in Honour of Dietrich von Rosen. Netherlands: Springer. 2020. p. 351-373 doi: 10.1007/978-3-030-56773-6_20, 10.1007/978-3-030-56773-6_20

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

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