Showing papers by "William E. Strawderman published in 1990"
TL;DR: In this paper, the authors present an expository development of Stein estimation with substantial emphasis on exact results for spherically symmetric distributions, showing that the improvement possible over the best invariant estimator via shrinkage estimation is not surprising but expected from a variety of perspectives.
Abstract: This paper presents an expository development of Stein estimation with substantial emphasis on exact results for spherically symmetric distributions. The themes of the paper are: a) that the improvement possible over the best invariant estimator via shrinkage estimation is not surprising but expected from a variety of perspectives; b) that the amount of shrinkage allowable to preserve domination over the best invariant estimator is, when properly interpreted, relatively free from the assumption of normality; and c) that the potential savings in risk are substantial when accompanied by good quality prior information.
60 citations
TL;DR: In this article, the Stein class of limited translation estimators were modified to be minimax estimators for the problem of estimating the mean vector under an arbitrary known quadratic loss function.
12 citations
Journal Article•
TL;DR: It is conjecture that investigators are often unsure of the possible bias in their auxiliary information, and thus the risk of the usual composite estimator can be greater than that of the sample mean.
Abstract: The usual method of combining sample data with auxiliary information is the familiar precision-weighted composite estimator. However, application of this estimator is straightforward only when the auxiliary information is unbiased. If this is not the case, and the bias is unaccounted for, then the risk of the usual composite estimator can be greater than that of the sample mean. We conjecture that investigators are often unsure of the possible bias in their auxiliary information (...)
8 citations
1 citations
TL;DR: For the simultaneous estimation of several Poisson parameters under the loss function, the authors proved the existence of sequential estimators which are better both in risk and sample size than the usual estimator (the sample mean) of a given fixed sample size.
Abstract: For the simultaneous estimation of several Poisson parameters under the loss function , we prove the existence of sequential estimators which are better both in risk (expected loss) and sample size than the usual estimator (the sample mean) of a given fixed sample size. Sequential versions of Clevenson-Zidek estimators are used to produce two-stage sequential estimators with the desired property.
1 citations