We study existence of unbiased estimators of risk for estimators of the location parameter of a spherically symmetric distribution, when a residual vector is available to estimate scale, under invariant quadratic loss. We show such existence often characterizes normality.

We consider estimation of the mean vector, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\theta $$</EquationSource> </InlineEquation>, of a spherically symmetric distribution with known scale parameter under quadratic loss and when a residual vector is available. We show minimaxity of generalized Bayes estimators corresponding to superharmonic priors with a non...</equationsource></inlineequation>

type="main" xml:id="insr12052-abs-0001" <title type="main">Summary</title>In this article, we develop a modern perspective on Akaike's information criterion and Mallows's C_p for model selection, and propose generalisations to spherically and elliptically symmetric distributions. Despite the differences in their respective...

For a vast array of general spherically symmetric location-scale models with a residual vector, we consider estimating the (univariate) location parameter when it is lower bounded. We provide conditions for estimators to dominate the benchmark minimax MRE estimator, and thus be minimax under...

Let X ~ N([theta],1), where [theta] [epsilon] [-m, m], for some m 0, and consider the problem of estimating [theta] with quadratic loss. We show that the Bayes estimator [delta]m, corresponding to the uniform prior on [-m, m], dominates [delta]0 (x) = x on [-m, m] and it also dominates the MLE...