Cover: Data Analysis Using Stein’s Estimator and Its Generalizations

Data Analysis Using Stein’s Estimator and Its Generalizations

Published 1974

by Bradley Efron, Carl N. Morris

Download eBook for Free

FormatFile SizeNotes
PDF file 2.1 MB

Use Adobe Acrobat Reader version 10 or higher for the best experience.

Stein's estimator for the mean of a multivariate normal distribution with uniformly lower mean squared error than the sample mean and several of its generalizations are presented briefly in an empirical Bayes context and applied to three examples with real data. These estimators perform much better than the classical estimators. The first application predicts final 1970 batting averages for 14 major league players from their early season performance. The predictions resulting from Stein's estimator are more accurate than the maximum likelihood estimator for every batter. Then toxoplasmosis prevalence rates for 36 El Salvador cities are estimated. The generalization of Stein's estimator used for this situation is substantially better than the usual estimator. Finally, in 51 situations a computer simulation is used to estimate the size of Pearson's chi-square test for comparing binomial means. Stein's estimator and its multivariate generalizations are approximately twice as efficient as the maximum likelihood estimator.

This report is part of the RAND report series. The report was a product of RAND from 1948 to 1993 that represented the principal publication documenting and transmitting RAND's major research findings and final research.

This document and trademark(s) contained herein are protected by law. This representation of RAND intellectual property is provided for noncommercial use only. Unauthorized posting of this publication online is prohibited; linking directly to this product page is encouraged. Permission is required from RAND to reproduce, or reuse in another form, any of its research documents for commercial purposes. For information on reprint and reuse permissions, please visit

RAND is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.