Asymptotics in Statistics: Some Basic Concepts (Springer Series in Statistics)

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This is the second edition of a coherent introduction to the subject of asymptotic statistics as it has developed over the past 50 years. It differs from the first edition in that it is now more 'reader friendly' and also includes a new chapter on Gaussian and Poisson experiments, reflecting their growing role in the field. Most of the subsequent chapters have been entirely rewritten and the nonparametrics of Chapter 7 have been amplified. The volume is not intended to replace monographs on specialized subjects, but will help to place them in a coherent perspective. It thus represents a link between traditional material - such as maximum likelihood, and Wald's Theory of Statistical Decision Functions -- together with comparison and distances for experiments. Much of the material has been taught in a second year graduate course at Berkeley for 30 years.

Asymptotics in Statistics: Some Basic Concepts (Springer Series in Statistics) Review

The first edition of this book was written in 1990. Le Cam was Professor of Statistics at the University of California at Berkeley where he taught since 1950. Grace Yang was one of his Ph.D. students who went on to become Professor of Statistics at the University of Maryland. They collaborated for many years. The book is based on lectures Le Cam gave at the University of Montreal in the summer of 1968. It was modified and first published in 1990 with some obsolete material deleted and sketches of new work over the 20 year interim added. This second edition was published just after Le Cam's death in April 2000. The second edition was revised to account for criticism of the first edition. The main criticism was that the book was difficult to understand even by a second year graduate student of statistics. This is clearly an advanced theoretical text but it includes many of Le Cam's important contributions and provides a unified theoretical treatment. Many typographical errors from the first edition have been removed. Chapter 4 is a new chapter on Gaussian and Poisson experiments.
It is by no means a complete treatment as the authors acknowledge in the Preface to the Second Edition material on von Mises differntiable functions, empirical processes and the recent developing school of Donoho and Johnstone is missing. The material on von Mises differentiable functions and empirical processes can be found in three recent texts by van der Vaart, van der Geer and Dudley. However, the authors did not feel prepared to summarize the Donoho and Johnstone work.

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