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Minimax Simple Bayes Estimators of a Normal Variance

Yuzo Maruyama

Abstract

This paper is a follow-up to Maruyama and Strawderman (2006, Journal of Statistical Planning and Inference), which identified a new class of generalized Bayes estimators with a particularly simple form for estimating a normal variance under entropy loss. Although their previous work established the Bayesianity of these estimators, it did not provide a closed-form result for their minimaxity. In this paper, we revisit the problem and establish a definitive closed-form minimaxity result for this class of simple Bayes estimators.

Minimax Simple Bayes Estimators of a Normal Variance

Abstract

This paper is a follow-up to Maruyama and Strawderman (2006, Journal of Statistical Planning and Inference), which identified a new class of generalized Bayes estimators with a particularly simple form for estimating a normal variance under entropy loss. Although their previous work established the Bayesianity of these estimators, it did not provide a closed-form result for their minimaxity. In this paper, we revisit the problem and establish a definitive closed-form minimaxity result for this class of simple Bayes estimators.
Paper Structure (3 sections, 1 theorem, 34 equations)

This paper contains 3 sections, 1 theorem, 34 equations.

Table of Contents

  1. Introduction
  2. Bayesianity
  3. Minimaxity

Key Result

Theorem 3.1

The simple Bayes estimator dominates $S/n$ when

Theorems & Definitions (3)

  • Theorem 3.1
  • proof
  • Remark 3.1