On empirical bayes estimation in the location family

R. J. Karunamuni, R. S. Singh, S. Zhang

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

This paper considers empirical Bayes (EB) squared error loss estimation (SELE) in the location family. That is, the component problem is the SELE of θ based on an observation Y having conditional (on θ) density of the form f0(y - θ) for some known density function f0. An EB estimator is constructed based on kernel type estimator of the unknown prior density using deconvolution techniques. It is shown that the proposed EB estimator is asymptotically optimal. Uniform rates of convergence of the regret are also exhibited. This paper presents a generalization to the existing results on the same problem considered for the normal (θ, 1) uniform (θ, θ + 1) and translated exponential (θ) distributions.

Original languageEnglish (US)
Pages (from-to)435-448
Number of pages14
JournalJournal of Nonparametric Statistics
Volume14
Issue number4
DOIs
StatePublished - Aug 2002

Keywords

  • Asymptotically optimal
  • Bayes
  • Empirical Bayes
  • Kernel density estimates
  • Location family
  • Squared error loss estimation

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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