Erich L. Lehmann - Böcker

This reprint of a classic reference describes rank tests and estimating procedures derived from them, and gives an account of their properties. All the tests discussed here are now available in a variety of statistical software packages.

It has been my good fortune to meet and get to know many remarkable people, mostly statisticians and mathematicians, and to derive much pleasure and benefit from these contacts. They were teachers, colleagues and students, and the following pages sketch their careers and our interactions. Also included are a few persons with whom I had little or no direct contact but whose ideas had a decisive influence on my work. To provide some coherence, the account is largely chronological and follows the steps of my own career. Taken together, these sketches provide a very personal picture of the dev- opment of statistical theory from the 1930s to the 1970s. It is the period between two revolutions: that of Fisher, Neyman, and Pearson, which laid the foundations for the classical statistical theory of that period; and the second revolution, forty years later, brought about by the advent of the computer, which turned statistics in new directions. The present account of this history is a highly selective one, which emphasizes the persons, institutions, and statistical topics that were close to my interests. One narrowing effect of this perspective stems from the fact that my career took place in the United States. As a consequence, the book focuses on American statisticians and institutions. Only the last two ch- ters discuss, briefly and very incompletely, developments in some other countries.

This second, much enlarged edition by Lehmann and Casella of Lehmann's classic text on point estimation maintains the outlook and general style of the first edition. All of the topics are updated. An entirely new chapter on Bayesian and hierarchical Bayesian approaches is provided, and there is much new material on simultaneous estimation. Each chapter concludes with a Notes section which contains suggestions for further study. The book is a companion volume to the second edition of Lehmann's "Testing Statistical Hypotheses". E.L. Lehmann is Professor Emeritus at the University of California, Berkeley. He is a member of the National Academy of Sciences and the American Academy of Arts and Sciences, and the recipient of honorary degrees from the University of Leiden, The Netherlands, and the University of Chicago. George Casella is the Liberty Hyde Bailey Professor of Biological Statistics in The College of Agriculture and Life Sciences at Cornell University. Casella has served as associate editor of The American Statistician, Statistical Science and JASA. He is currently the Theory and Methods Editor of JASA.Casella has authored two other textbooks (Statistical Inference, 1990, with Roger Berger and Variance Components, 1992, with Shayle A. Searle and Charles McCulloch). He is a fellow of the IMS and ASA, and an elected fellow of the ISI. Also available: E.L. Lehmann, Testing Statistical Hypotheses Second Edition, Springer- Verlag New York, Inc., 0-387-94919-4.

Since the publication in 1983 of Theory of Point Estimation, much new work has made it desirable to bring out a second edition.

The Third Edition of Testing Statistical Hypotheses brings it into consonance with the Second Edition of its companion volume on point estimation (Lehmann and Casella, 1998) to which we shall refer as TPE2. We won’t here comment on the long history of the book which is recounted in Lehmann (1997) but shall use this Preface to indicate the principal changes from the 2nd Edition. The present volume is divided into two parts. Part I (Chapters 1–10) treats small-sample theory, while Part II (Chapters 11–15) treats large-sample theory. The preface to the 2nd Edition stated that “the most important omission is an adequate treatment of optimality paralleling that given for estimation in TPE.” We shall here remedy this failure by treating the di?cult topic of asymptotic optimality (in Chapter 13) together with the large-sample tools needed for this purpose (in Chapters 11 and 12). Having developed these tools, we use them in Chapter 14 to give a much fuller treatment of tests of goodness of ?tthan was possible in the 2nd Edition, and in Chapter 15 to provide an introduction to the bootstrap and related techniques. Various large-sample considerations that in the Second Edition were discussed in earlier chapters now have been moved to Chapter 11.