Asymptotic Distribution of the Random Regret Risk for Selecting Exponential Populations

Abstract

In this paper empirical Bayes methods are applied to construct selection rules for the selection of all good exponential distributions. We modify the selection rule introduced and studied by Gupta and Liang (1996) who proved that the regret risk ER(n) converges to zero with rate 0(n(exp -lambda/2), 0 < lambda less than or equal 2. The aim of this paper is to prove a limit theorem for the random regret risk R(n). It is shown that nR(n) tends in distribution to a linear combination of independent X(exp 2)- distributed random variables. This result especially implies that under weak conditions the random regret risk is of order Op(1/n).

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1998
Accession Number
ADA358189

Entities

People

  • Friedrich Liese
  • Shanti Gupta

Organizations

  • Purdue University

Tags

Communities of Interest

  • Human Systems

DTIC Thesaurus Topics

  • Abstracts
  • Asymptotic Normality
  • Consistency
  • Convergence
  • Data Science
  • Decision Theory
  • Estimators
  • Information Science
  • Military Research
  • New York
  • Order Statistics
  • Probability
  • Random Variables
  • Statistical Decision Theory
  • Statistics
  • Stochastic Processes
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Statistical inference.