摘要：For estimating the median θ of a spherically symmetric univariate distribution under squared error loss, when θ is known to be restricted to an interval [ −m,m ], m known, we derive sufficient conditions for estimators δ to dominate the maximum likelihood estimator δ mle. Namely: (i) we identify a large class of models where for sufficiently small m , all Bayesian estimators with respect to symmetric about 0 priors supported on [ −m,m ] dominate δ mle, and (ii) we provide for Bayesian estimators δπ sufficient dominance conditions of the form m ≤ cπ , which are applicable to various models and priors π . In terms of the models, applications include Cauchy and Student distributions, densities which are logconvex on ( θ,∞ ) including scale mixtures of Laplace distributions, and logconcave on ( θ, ∞ ) densities with logconvex on ( θ,∞ ) first derivatives such as normal, logistic, Laplace and hyperbolic secant, among others. In terms of priors π which lead to dominating δπ 's in (ii) , applications include the uniform density, as well as symmetric densities about 0, which are also absolutely continuous, nondecreasing and logconcave on (0 ,m ).
关键词：Bayes estimator;Cauchy and Student models;dominance;logconcave densities;logconvex densities;maximum likelihood estimator;restricted parameter space;scale mixture of Laplace densities;squared error loss;symmetric location families
