Optimal Rate of Convergence of Monotone Empirical Bayes Tests for a Normal Mean

Abstract

This paper studies monotone empirical Bayes tests for a normal mean under a linear loss. The optimal rate of convergence of the monotone empirical Bayes tests is obtained. Applying a few techniques and using the non-uniform estimate of the remainder in the central limit theorem, we are able to construct a monotone empirical Bayes test and show that it achieves the best possible rate over a broad class of prior distributions, while the best possible rate is obtained through an idea of Donoho and Liu by constructing the "hardest two-point subproblem". This answers the question raised recently by Karunamuni and Liang. The result indicates that n(exp -1) may not be an attainable lower bound for the monotone empirical Bayes tests in the continuous one- parameter exponential family. A method to construct the monotone empirical Bayes test achieving the optimal rate is also discussed in this paper.

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 2001
Accession Number
ADA393544

Entities

People

  • Jianjun Li
  • Shanti Gupta

Organizations

  • Purdue University

Tags

Communities of Interest

  • Human Systems

DTIC Thesaurus Topics

  • Abstracts
  • Classification
  • Computations
  • Construction
  • Convergence
  • Kernel Functions
  • Military Research
  • Normal Distribution
  • Probability
  • Random Variables
  • Security
  • Statistics
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Fields of Study

  • Mathematics

Readers

  • Operations Research
  • Statistical inference.