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

Tatsuya Kubokawa, William E. Strawderman and Ryota Yuasa

Communications in Statistics - Theory and Methods, 2020, vol. 49, issue 8, 2008-2024

Abstract: 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.

Date: 2020
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DOI: 10.1080/03610926.2019.1568481

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