Empirical Bayes two-action problem for the continuous one-parameter exponential family with errors in variables

Rohana J. Karunamuni, Shunpu Zhang

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

In this paper we study the empirical Bayes linear-loss two-action problem for the continuous one-parameter exponential family when the observed data are contaminated (errors in variables). A new empirical Bayes testing rule is constructed, and its asymptotic optimality uniformly over a class of prior distributions is established. Uniform rates of convergence of the corresponding regret (excess risk), which depends on the type of the error distribution, are also obtained for two types of error distributions. Our results are compared with the 'pure' observed data results of the literature.

Original languageEnglish (US)
Pages (from-to)437-449
Number of pages13
JournalJournal of Statistical Planning and Inference
Volume113
Issue number2
DOIs
StatePublished - May 1 2003

Keywords

  • Asymptotically optimal
  • Empirical Bayes
  • Errors in variables
  • Rates of convergence

ASJC Scopus subject areas

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

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