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>

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.

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...

<Para ID="Par1">From an observable <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$(X,U)$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mo stretchy="false">(</mo> <mi>X</mi> <mo>,</mo> <mi>U</mi> <mo stretchy="false">)</mo> </mrow> </math> </EquationSource> </InlineEquation> in <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$\mathbb R^p \times \mathbb R^k$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <msup> <mi mathvariant="double-struck">R</mi> <mi>p</mi> </msup> <mo>×</mo> <msup> <mi mathvariant="double-struck">R</mi> <mi>k</mi> </msup> </mrow> </math> </EquationSource> </InlineEquation>, we consider estimation of an unknown location parameter <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$\theta \in \mathbb R^p$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi mathvariant="italic">θ</mi> <mo>∈</mo> <msup> <mi mathvariant="double-struck">R</mi> <mi>p</mi> </msup> </mrow> </math> </EquationSource> </InlineEquation> under two distributional settings: the density of <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$(X,U)$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mo stretchy="false">(</mo> <mi>X</mi> <mo>,</mo> <mi>U</mi> <mo stretchy="false">)</mo> </mrow> </math> </EquationSource> </InlineEquation> is...</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></para>

Families of minimax estimators are found for the location parameter of a p-variate (pgt; or = 3) spherically symmetric unimodal(s.s.u.)distribution with respect to general quadratic loss. The estimators of James and Stein, Baranchik, Bock and Strawderman are all considered for this general...

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...

This paper is primarily concerned with extending the results of Stein to spherically symmetric distributions. Specifically, when X ∼f(||X - θ||2), we investigate conditions under which estimators of the form X ag(X) dominate X for loss functions ||δ- θ||2 and loss functions which are...

For p 4 and one observation X on a p-dimensional spherically symmetric distribution, minimax estimators of Theta whose risks are smaller than the risk of X (the best invariant estimator) are found when the loss is a nondecreasing concave function of quadratic loss. For n observations X1, X2, ......