Showing papers by "William E. Strawderman published in 2008"
TL;DR: In this article, the generalized Bayes estimator is shown to be minimax and dominates the usual minimax estimator under certain conditions on the spherically symmetric prior.
20 citations
TL;DR: In this article, the authors extend the results of Strawderman [Minimax estimation of location parameters for certain spherically symmetric distribution, J. Multivariate Anal. 4 (1974) 255-264] in a manner similar to that of Maruyama [Admissible minimax estimators of a mean vector of scale mixtures of multivariate normal distributions] but somewhat more in the spirit of Fourdrinier et al.
14 citations
TL;DR: In this paper, an increasing sequence of bounds on the shrinkage constant of Stein-type estimators were given for the case of spherical symmetry, spherical symmetry and unimodality, and scale mixtures of normals.
9 citations
TL;DR: The frequentist performance of the Bayesian HPD credible set associated with priors which are truncations of flat priors onto the restricted parameter space is investigated and it is shown that this minimum coverage is bounded between $1-\frac{3\alpha}{2}+\frac{\alpha^2}{1+\alpha}.
Abstract: For estimating a lower bounded location or mean parameter for a symmetric and logconcave density, we investigate the frequentist performance of the $100(1-\alpha)%$ Bayesian HPD credible set associated with priors which are truncations of flat priors onto the restricted parameter space. Various new properties are obtained. Namely, we identify precisely where the minimum coverage is obtained and we show that this minimum coverage is bounded between $1-\frac{3\alpha}{2}$ and $1-\frac{3\alpha}{2}+\frac{\alpha^2}{1+\alpha}$; with the lower bound $1-\frac{3\alpha}{2}$ improving (for $\alpha \leq 1/3$) on the previously established ([9]; [8]) lower bound $\frac{1-\alpha}{1+\alpha}$. Several illustrative examples are given.
7 citations
TL;DR: For estimating a lower bounded location or mean parameter for a symmetric and logconcave density, this article investigated the frequentist performance of the 100(1−α)% Bayesian HPD credible set associated with priors which are truncations of flat priors onto the restricted parameter space.
Abstract: For estimating a lower bounded location or mean parameter for a symmetric and logconcave density, we investigate the frequentist performance of the 100(1−α)% Bayesian HPD credible set associated with priors which are truncations of flat priors onto the restricted parameter space. Various new properties are obtained. Namely, we identify precisely where the minimum coverage is obtained and we show that this minimum coverage is bounded between $1-\frac{3\alpha}{2}$ and $1-\frac{3\alpha}{2}+\frac{\alpha^{2}}{1+\alpha}$; with the lower bound $1-\frac{3\alpha}{2}$ improving (for α≤1/3) on the previously established ([9]; [8]) lower bound $\frac{1-\alpha}{1+\alpha}$. Several illustrative examples are given.
7 citations
TL;DR: In this article, the authors considered the problem of finding an unbiased estimator of the risk difference between δ ( X ) and δ 0 (X ) under the quartic loss ∑ i = 1 p ( δ i - θ i ) 4 for p ⩾ 3.
6 citations