Bayes and empirical Bayes estimation with errors in variables

Shunpu Zhang, Rohana J. Karunamuni

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


Suppose that the random variable X is distributed according to exponential families of distributions, conditional on the parameter θ. Assume that the parameter θ has a (prior) distribution G. Because of the measurement error, we can only observe Y = X + ε, where the measurement error ε is independent of X and has a known distribution. This paper considers the squared error loss estimation problem of θ based on the contaminated observation Y. We obtain an expression for the Bayes estimator when the prior G is known. For the case G is completely unknown, an empirical Bayes estimator is proposed based on a sequence of observations Y1,Y2,...,Yn, where Yi's are i.i.d. according to the marginal distribution of Y. It is shown that the proposed empirical Bayes estimator is asymptotically optimal.

Original languageEnglish (US)
Pages (from-to)23-34
Number of pages12
JournalStatistics and Probability Letters
Issue number1
StatePublished - Apr 15 1997


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

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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