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Asymptotic Theory of Statistics and Probability

  • Kartonierter Einband
  • 722 Seiten
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This unique book delivers an encyclopedic treatment of classic as well as contemporary large sample theory. It deals with both sta... Weiterlesen
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This unique book delivers an encyclopedic treatment of classic as well as contemporary large sample theory. It deals with both statistical problems and probabilistic issues and tools. The book's detailed coverage is written in an extremely lucid style.

This book developed out of my year-long course on asymptotic theory at Purdue University. To some extent, the topics coincide with what I cover in that course. There are already a number of well-known books on asy- totics. This book is quite different. It covers more topics in one source than areavailableinanyothersinglebookonasymptotictheory. Numeroustopics covered in this book are available in the literature in a scattered manner, and they are brought together under one umbrella in this book. Asymptotic theory is a central unifying theme in probability and statistics. My main goal in writing this book is to give its readers a feel for the incredible scope and reach of asymptotics. I have tried to write this book in a way that is accessible and to make the reader appreciate the beauty of theory and the insights that only theory can provide. Essentially every theorem in the book comes with at least one reference, preceding or following the statement of the theorem. In addition, I have p- vided a separate theorem-by-theorem reference as an entry on its own in the front of the book to make it extremely convenient for the reader to ?nd a proof that was not provided in the text. Also particularly worth mentioning is a collection of nearly 300 practically useful inequalities that I have c- lected together from numerous sources. This is appended at the very end of the book.

This unique book provides unmatched coverage of topics of interest to a very broad spectrum of statisticians and also probabilists. The book can be used in multiple roles. It can be used as a graduate text with a huge choice of topics for the instructor, as an invaluable general purpose reference, for independent reading by students and researchers, and for getting an overview of the latest developments in some of the most contemporary topics, such as false discovery, treatment of dependent data, and the bootstrap. There is no other book in large sample theory that matches this book in coverage, exercises and examples, bibliography, and lucid conceptual discussion of issues and theorems.

Basic Convergence Concepts and Theorems.- Metrics, Information Theory, Convergence, and Poisson Approximations.- More General Weak and Strong Laws and the Delta Theorem.- Transformations.- More General Central Limit Theorems.- Moment Convergence and Uniform Integrability.- Sample Percentiles and Order Statistics.- Sample Extremes.- Central Limit Theorems for Dependent Sequences.- Central Limit Theorem for Markov Chains.- Accuracy of Central Limit Theorems.- Invariance Principles.- Edgeworth Expansions and Cumulants.- Saddlepoint Approximations.- U-statistics.- Maximum Likelihood Estimates.- M Estimates.- The Trimmed Mean.- Multivariate Location Parameter and Multivariate Medians.- Bayes Procedures and Posterior Distributions.- Testing Problems.- Asymptotic Efficiency in Testing.- Some General Large-Deviation Results.- Classical Nonparametrics.- Two-Sample Problems.- Goodness of Fit.- Chi-square Tests for Goodness of Fit.- Goodness of Fit with Estimated Parameters.- The Bootstrap.- Jackknife.- Permutation Tests.- Density Estimation.- Mixture Models and Nonparametric Deconvolution.- High-Dimensional Inference and False Discovery.- A Collection of Inequalities in Probability, Linear Algebra, and Analysis.


Titel: Asymptotic Theory of Statistics and Probability
EAN: 9781461498841
ISBN: 978-1-4614-9884-1
Format: Kartonierter Einband
Herausgeber: Springer, Berlin
Genre: Mathematik
Anzahl Seiten: 722
Gewicht: 1139g
Größe: H42mm x B238mm x T156mm
Jahr: 2014
Auflage: 2008

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