Minimax Rules Under Zero-One Loss for a Restricted Location
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چکیده
Minimax Rules Under Zero-One Loss In this paper, we obtain minimax and near-minimax nonrandomized decision rules under zeroone loss for a restricted location parameter of an absolutely continuous distribution. Two types of rules are addressed: monotone and nonmonotone. A complete-class theorem is proved for the monotone case. This theorem extends the previous work of Zeytinoglu and Mintz (1984) to the case of 2e-MLR sampling distributions. A class of continuous monotone nondecreasing rules is defined. This class contains the monotone minimax rules developed in this paper. It is shown that each rule in this class is Bayes with respect to nondenumerably many priors. A procedure for generating these priors is presented. Nonmonotone near-minimax almost-equalizer rules are derived for problems characterized by non2e-MLR distributions. The derivation is based on the evaluation of a distribution-dependent function Qc. The methodological importance of this function is that it is used to unify the discreteand continuous-parameter problems, and to obtain a lower bound on the minimax risk for the non2e-MLR case.
منابع مشابه
Minimax Rules under Zero-one Loss for a Restricted Location Parameter 1
Minimax Rules Under Zero-One Loss In this paper we study the existence, structure and computation of minimax and near-minimax rules under zero-one loss for a restricted location parameter of an absolutely continuous distribution.
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