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Bayes and empirical Bayes estimation with errors in variables

โœ Scribed by Shunpu Zhang; Rohana J. Karunamuni

Book ID
104302487
Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
544 KB
Volume
33
Category
Article
ISSN
0167-7152

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โœฆ Synopsis

Suppose that the random variable X is distributed according to exponential families of distributions, conditional on the parameter 0. Assume that the parameter 0 has a (prior) distribution G. Because of the measurement error, we can only observe Y = X+e, where the measurement error e is independent of X and has a known distribution. This paper considers the squared error loss estimation problem of 0 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 ..... Y,, where Y~'s are i.i.d, according to the marginal distribution of Y. It is shown that the proposed empirical Bayes estimator is asymptotically optimal.

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