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
δmle. 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
δmle, 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).
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