On empirical bayes estimation in the location family

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

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 1 2002

Fingerprint

Empirical Bayes Estimation
Empirical Bayes Estimator
Squared Error Loss
Empirical Bayes
Regret
Deconvolution
Asymptotically Optimal
Exponential distribution
Density Function
Rate of Convergence
kernel
Estimator
Unknown
Family
Form
Observation
Generalization

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

Cite this

On empirical bayes estimation in the location family. / Karunamuni, R. J.; Singh, R. S.; Zhang, Shunpu.

In: Journal of Nonparametric Statistics, Vol. 14, No. 4, 01.08.2002, p. 435-448.

Research output: Contribution to journalArticle

Karunamuni, R. J. ; Singh, R. S. ; Zhang, Shunpu. / On empirical bayes estimation in the location family. In: Journal of Nonparametric Statistics. 2002 ; Vol. 14, No. 4. pp. 435-448.
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