Shrinkage estimation of location parameters in a multivariate skew-normal distribution

TY - JOUR

T1 - Shrinkage estimation of location parameters in a multivariate skew-normal distribution

AU - Kubokawa, Tatsuya

AU - Strawderman, William E.

AU - Yuasa, Ryota

N1 - Funding Information: We would like to thank the Editor, the Associate Editor and the reviewer for valuable comments and helpful suggestions which led to an improved version of this paper. This research was supported in part by Grant-in-Aid for Scientific Research from Japan Society for the Promotion of Science (# 18K11188, # 15H01943 and # 26330036 to Tatsuya Kubokawa). This work was partially supported by a grant from the Simons Foundation (#418098 to William Strawderman). Publisher Copyright: © 2019, © 2019 Taylor & Francis Group, LLC.

PY - 2020/4/17

Y1 - 2020/4/17

N2 - This paper studies decision theoretic properties of Stein type shrinkage estimators in simultaneous estimation of location parameters in a multivariate skew-normal distribution with known skewness parameters under a quadratic loss. The benchmark estimator is the best location equivariant estimator which is minimax. A class of shrinkage estimators improving on the best location equivariant estimator is constructed when the dimension of the location parameters is larger than or equal to four. An empirical Bayes estimator is also derived, and motivated from the Bayesian procedure, we suggest a simple skew-adjusted shrinkage estimator and show its dominance property. The performances of these estimators are investigated by simulation.

AB - This paper studies decision theoretic properties of Stein type shrinkage estimators in simultaneous estimation of location parameters in a multivariate skew-normal distribution with known skewness parameters under a quadratic loss. The benchmark estimator is the best location equivariant estimator which is minimax. A class of shrinkage estimators improving on the best location equivariant estimator is constructed when the dimension of the location parameters is larger than or equal to four. An empirical Bayes estimator is also derived, and motivated from the Bayesian procedure, we suggest a simple skew-adjusted shrinkage estimator and show its dominance property. The performances of these estimators are investigated by simulation.

KW - Decision theory

KW - dominance result

KW - empirical Bayes

KW - mean mixture of normal distributions

KW - minimaxity

KW - multivariate skew-normal distribution

KW - quadratic loss function

KW - risk function

UR - http://www.scopus.com/inward/record.url?scp=85061027903&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85061027903&partnerID=8YFLogxK

U2 - https://doi.org/10.1080/03610926.2019.1568481

DO - https://doi.org/10.1080/03610926.2019.1568481

M3 - Article

SN - 0361-0926

VL - 49

SP - 2008

EP - 2024

JO - Communications in Statistics - Theory and Methods

JF - Communications in Statistics - Theory and Methods

IS - 8

ER -