Minimax Estimation of a Bounded Discrete Parameter
نویسندگان
چکیده
For a vast class of discrete model families with cdf’s Fθ, and for estimating θ under squared error loss under a constraint of the type θ ∈ [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 ≤ 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.
منابع مشابه
Minimax Estimator of a Lower Bounded Parameter of a Discrete Distribution under a Squared Log Error Loss Function
The problem of estimating the parameter ?, when it is restricted to an interval of the form , in a class of discrete distributions, including Binomial Negative Binomial discrete Weibull and etc., is considered. We give necessary and sufficient conditions for which the Bayes estimator of with respect to a two points boundary supported prior is minimax under squared log error loss function....
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