Minimax estimation of a bounded parameter of a discrete distribution

Éric Marchand and Ahmad Parsian

Statistics & Probability Letters, 2006, vol. 76, issue 6, 547-554

Abstract: For a vast class of discrete model families with cdf's F[theta], and for estimating [theta] under squared error loss under a constraint of the type [theta][set membership, variant][0,m], we present a general and unified development concerning the minimaxity of a boundary supported prior Bayes estimator. While the sufficient conditions obtained are of the expected form m[less-than-or-equals, slant]m(F), the approach presented leads, in many instances, to both necessary and sufficient conditions, and/or explicit values for m(F). Finally, the scope of the results is illustrated with various examples that, not only include several common distributions (e.g., Poisson, Binomial, Negative Binomial), but many others as well.

Keywords: Minimax; estimation; Restricted; parameter; space; Discrete; distributions; Squared; error; loss (search for similar items in EconPapers)
Date: 2006
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