Improving on the James-Stein Positive-Part Estimator

The purpose of this paper is to give an explicit estimator dominating the positive-part James-Stein rule. The James-Stein estimator improves on the "usual" estimator X of a multivariate normal mean vector θ if the dimension p of the problem is at least 3. It has been known since at least 1...

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Bibliographic Details
Published in:The Annals of statistics 1994-09, Vol.22 (3), p.1517-1538
Main Authors: Shao, Peter Yi-Shi, Strawderman, William E.
Format: Article
Language:English
Subjects:
62C99
62F10
62H99
Decision theory
Degrees of freedom
Estimators
Estimators for the mean
Exact sciences and technology
Gaussian distributions
Integers
location parameters
Mathematics
Minimaxity
Parametric Models and Inference
Probability and statistics
Sciences and techniques of general use
Sine function
squared error loss
Statistics
Unbiased estimators
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Summary:The purpose of this paper is to give an explicit estimator dominating the positive-part James-Stein rule. The James-Stein estimator improves on the "usual" estimator X of a multivariate normal mean vector θ if the dimension p of the problem is at least 3. It has been known since at least 1964 that the positive-part version of this estimator improves on the James-Stein estimator. Brown's 1971 results imply that the positive-part version is itself inadmissible although this result was assumed to be true much earlier. Explicit improvements, however, have not previously been found; indeed, 1988 results of Bock and of Brown imply that no estimator dominating the positive-part estimator exists whose unbiased estimator of risk is uniformly smaller than that of the positive-part estimator.
ISSN:0090-5364
2168-8966
DOI:10.1214/aos/1176325640