A Gaussian sequence approach for proving minimaxity: A Review

Yuzo Maruyama, William E. Strawderman

Research output: Contribution to journalReview article

Abstract

This paper reviews minimax best equivariant estimation in three invariant estimation problems: a location parameter, a scale parameter and a (Wishart) covariance matrix. We briefly review development of the best equivariant estimator as a generalized Bayes estimator relative to right invariant Haar measure in each case. Then we prove minimaxity of the best equivariant procedure by giving a least favorable prior sequence based on non-truncated Gaussian distributions. The results in this paper are all known, but we bring a fresh and somewhat unified approach by using, in contrast to most proofs in the literature, a smooth sequence of non truncated priors. This approach leads to some simplifications in the minimaxity proofs.

Original languageEnglish (US)
Pages (from-to)256-270
Number of pages15
JournalJournal of Statistical Planning and Inference
Volume211
DOIs
StatePublished - Mar 2021

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

Keywords

  • Equivariance
  • Invariance
  • Least favorable prior
  • Minimaxity

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