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

Tatsuya Kubokawa, William E. Strawderman, Ryota Yuasa

Research output: Contribution to journalArticle

1 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)2008-2024
Number of pages17
JournalCommunications in Statistics - Theory and Methods
Volume49
Issue number8
DOIs
StatePublished - Apr 17 2020

All Science Journal Classification (ASJC) codes

  • Statistics and Probability

Keywords

  • Decision theory
  • dominance result
  • empirical Bayes
  • mean mixture of normal distributions
  • minimaxity
  • multivariate skew-normal distribution
  • quadratic loss function
  • risk function

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