Pitman's Measure of Closeness: A Comparison of Statistical Estimators

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SIAM, 1993 - Mathematics - 226 pages
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Pitman's Measure of Closeness (PMC) is simply an idea whose time has come. Certainly there are many different ways to estimate unknown parameters, but which method should you use? Posed as an alternative to the concept of mean-squared-error, PMC is based on the probabilities of the closeness of competing estimators to an unknown parameter. Renewed interest in PMC over the last 20 years has motivated the authors to produce this book, which explores this method of comparison and its usefulness. Written with research oriented statisticians and mathematicians in mind, but also considering the needs of graduate students in statistics courses, this book provides a thorough introduction to the methods and known results associated with PMC. Following a foreword by C .R. Rao, the first three chapters focus on basic concepts, history, controversy, paradoxes and examples associated with the PMC criterion.
  

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Contents

Introduction
1
Development of Pitmans Measure of Closeness
25
Anomalies with PMC
65
Pairwise Comparisons
101
PitmanClosest Estimators
135
Asymptotics and PMC
169
Bibliography
211
Index
223
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Page 215 - HODGES, JL, JR. and LEHMANN, EL, 1951. Some applications of the Cramer-Rao inequality. Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, University of California Press 13-22.
Page 211 - The Concept of Asymptotic Efficiency and Higher Order Asymptotic Efficiency in Statistical Estimation Theory.

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About the author (1993)

Pranab K. Sen is the Cary C. Boshamer Professor of Biostatistics and Professor of Statistics and Operations Research at the University of North Carolina, Chapel Hill. He is the author or co-author of numerous textbooks in statistics and biostatistics, and editor or co-editor of numerous volumes in the same field. He has more than 600 publications in leading statistics journals and has supervised 83 doctoral students. Sen is a Fellow of both the Institute of Mathematical Statistics and the American Statistical Association. In 2002 he was Senior Noether Awardee for his lifelong contributions to nonparametrics and received the Commemoration Medal from the Czech Union of Physicists and Mathematicians in 1998.

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