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“This book is a photographic reproduction of the book of the same title published in 1981, for which there has been continuing demand on account of its accessible technical level. Its appearance also helped generate considerable subsequent work on inhomogeneous products of matrices. This printing adds an additional bibliography on coefficients of ergodicity and a list of corrigenda. Eugene Seneta received his Ph.D. in 1968 from the Australian National University. He left Canberra in 1979 to become Professor and Head of the Department of Mathematical Statistics at the University of Sydney. He has been a regular visitor to the United States, most frequently to the University of Virginia. Now Emeritus Professor at the University of Sydney, he has recently developed a renewed interest in financial mathematics. He was elected Fellow of the Australian Academy of Science in 1985 and awarded the Pitman Medal of the Statistical Society of Australia for his distinguished research contributions. The first edition of this book, entitled Non-Negative Matrices, appeared in 1973, and was followed in 1976 by his Regularly Varying Functions in the Springer Lecture Notes in Mathematics, later translated into Russian. Both books were pioneering in their fields. In 1977, Eugene Seneta coauthored (with C. C. Heyde ) I.J. Bienaymé : Statistical Theory Anticipated, which is effectively a history of probability and statistics in the 19th century, and in 2001 co-edited with the same colleague Statisticians of the Centuries, both published by Springer. Having served on the editorial board of the Encyclopedia of Statistical Science, he is currently Joint Editor of the International Statistical Review.” [Publisher]

Stochastic processes --- Non-negative matrices --- Markov processes --- Matrices non négatives --- Markov, Processus de --- Matrices non négatives --- EPUB-LIV-FT LIVSTATI SPRINGER-B --- Matrices --- Probabilités. --- Probabilities --- Probabilités

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This book is an encyclopedic treatment of classic as well as contemporary large sample theory, dealing with both statistical problems and probabilistic issues and tools. It is written in an extremely lucid style, with an emphasis on the conceptual discussion of the importance of a problem and the impact and relevance of the theorems. The book has 34 chapters over a wide range of topics, nearly 600 exercises for practice and instruction, and another 300 worked out examples. It also includes a large compendium of 300 useful inequalities on probability, linear algebra, and analysis that are collected together from numerous sources, as an invaluable reference for researchers in statistics, probability, and mathematics. It can be used as a graduate text, as a versatile research reference, as a source for independent reading on a wide assembly of topics, and as a window to learning the latest developments in contemporary topics. The book is unique in its detailed coverage of fundamental topics such as central limit theorems in numerous setups, likelihood based methods, goodness of fit, higher order asymptotics, as well as of the most modern topics such as the bootstrap, dependent data, Bayesian asymptotics, nonparametric density estimation, mixture models, and multiple testing and false discovery. It provides extensive bibliographic references on all topics that include very recent publications. Anirban DasGupta is Professor of Statistics at Purdue University. He has also taught at the Wharton School of the University of Pennsylvania, at Cornell University, and at the University of California at San Diego. He has been on the editorial board of the Annals of Statistics since 1998 and has also served on the editorial boards of the Journal of the American Statistical Association, International Statistical Review, and the Journal of Statistical Planning and Inference. He has edited two monographs in the lecture notes monograph series of the Institute of Mathematical Statistics, is a Fellow of the Institute of Mathematical Statistics and has 70 refereed publications on theoretical statistics and probability in major journals.

Mathematical statistics --- Asymptotic theory --- Asymptotic theory. --- Statistique mathématique --- Théorie asymptotique --- EPUB-LIV-FT LIVSTATI SPRINGER-B --- Mathematical statistics - Asymptotic theory

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Nonparametric statistics --- Mathematical statistics --- Statistique non-paramétrique --- EPUB-LIV-FT LIVSTATI SPRINGER-B --- Nonparametric statistics. --- 519.234 --- Distribution-free statistics --- Statistics, Distribution-free --- Statistics, Nonparametric --- 519.234 Non-parametric methods --- Non-parametric methods

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This book consists of four hundred exercises in mathematical statistics and their solutions, over 95% of which are in the author's Mathematical Statistics, Second Edition (Springer, 2003). For students preparing for work on a Ph.D. degree in statistics and instructors of mathematical statistics courses, this useful book provides solutions to train students for their research ability in mathematical statistics and presents many additional results and examples that complement any text in mathematical statistics. To develop problem-solving skills, two solutions and/or notes of brief discussions accompany a few exercises. The exercises are grouped into seven chapters with titles matching those in the author's Mathematical Statistics. On the other hand, the book is stand-alone because exercises and solutions are comprehensible independently of their source, and notation and terminology are explained in the front of the book. Readers are assumed to have a good knowledge in advanced calculus. A course in real analysis or measure theory is highly recommended. If this book is used with a statistics textbook that does not include probability theory, then knowledge in measure-theoretic probability theory is required. Jun Shao is Professor of Statistics at the University of Wisconsin, Madison.

Mathematical statistics --- Statistique mathématique --- Problems, exercises, etc. --- Problèmes et exercices --- Mathematical statistics. --- Mathematical statistics - Problems, exercises, etc. --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- Statistics --- Statistique mathématique --- Problèmes et exercices --- EPUB-LIV-FT LIVSTATI SPRINGER-B --- Statistics. --- Statistical Theory and Methods. --- Statistical inference --- Statistics, Mathematical --- Probabilities --- Sampling (Statistics) --- Statistical methods --- Statistics . --- Statistical analysis --- Statistical data --- Statistical science --- Econometrics

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Twenty-?ve years have passed since the publication of the Russian version of the book Estimation of Dependencies Based on Empirical Data (EDBED for short). Twen- ?ve years is a long period of time. During these years many things have happened. Looking back, one can see how rapidly life and technology have changed, and how slow and dif?cult it is to change the theoretical foundation of the technology and its philosophy. I pursued two goals writing this Afterword: to update the technical results presented in EDBED (the easy goal) and to describe a general picture of how the new ideas developed over these years (a much more dif?cult goal). The picture which I would like to present is a very personal (and therefore very biased) account of the development of one particular branch of science, Empirical - ference Science. Such accounts usually are not included in the content of technical publications. I have followed this rule in all of my previous books. But this time I would like to violate it for the following reasons. First of all, for me EDBED is the important milestone in the development of empirical inference theory and I would like to explain why. S- ond, during these years, there were a lot of discussions between supporters of the new 1 paradigm (now it is called the VC theory ) and the old one (classical statistics).

Estimation theory. --- Théorie de l'estimation --- Estimation theory --- Mathematical Statistics --- Computer Science --- Mechanical Engineering - General --- Mechanical Engineering --- Engineering & Applied Sciences --- Mathematics --- Physical Sciences & Mathematics --- Information Technology --- Artificial Intelligence --- Théorie de l'estimation --- EPUB-LIV-FT LIVSTATI SPRINGER-B --- Estimating techniques --- Mathematics. --- Applied mathematics. --- Engineering mathematics. --- Applications of Mathematics. --- Least squares --- Mathematical statistics --- Stochastic processes --- Math --- Science