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

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.

'This monograph was written by three internationally reputed statisticians who have been instrumental in creating the recent interest in Pitman's measure of closeness (PMC).... There are several motivating and nontechnical examples that are easy to follow. Some material from Chapters 1, 2, and 3 could be used in a first-year graduate level course, whereas Chapters 4, 5, and 6 could be discussed in a graduate level course. Implicitly, in addition to providing answers to some difficult questions, the authors pose many important and challenging research problems for future research.... I believe that this is a useful monograph for a researcher interested in the PMC criterion. It summarizes and unifies some of the important results in the area.' Shyamal D. Peddada, Journal of Applied Statistical Applications

'The authors have written an interesting and lively account of recent developments in the study of Pitman Closeness. The book gathers together much of what is known in the area and presents it in a balanced manner. It is the best and most complete source of material on Pitman's measure of closeness and should be most useful to anyone interested in the subject.' William E. Strawderman, Professor of Statistics, Rutgers University

'Nicely presents history of Pitman's measure of closeness (PMC), applications to single-parameter estimation problems, PMC anomalies, and asymtotics.' American Mathematical Monthly

'This recent monograph assembles the widespread material concerning Pitman's measure of closeness (PMC) that is available in the literature and much of which is not widely known ... the authors recommend Pitman closeness as an interesting alternative criterion for comparing estimators. They investigate the usefulness of the PMC for this purpose, and discuss the properties of 'Pitman-closest' estimators. This is done both from a frequentist and Bayesian point of view, in both small-sample and large-sample settings. The book contains many fascinating examples and results.' E. L. Lehmann, Short Book Reviews

' ... a comprehensive survey of recent contributions to the subject. It discusses the merits and deficiencies of PMC, throws light on recent controversies, and formulates new problems for further research. Finally, there is a need for such a book, as PMC is not generally discussed in statistical texts. Its role in estimation theory and its usefulness to the decision maker are not well known. . . The contributions by the authors of this book have been especially illuminating in resolving some of the controversies surrounding PMC.' C. R. Rao, from the foreword