Asymptotics In Statistics And Probability

Author : Anirban DasGupta
Publisher : Springer Science & Business Media
Page : 726 pages
File Size : 51,6 Mb
Release : 2008-03-07
Category : Mathematics
ISBN : 9780387759708

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Asymptotic Theory of Statistics and Probability by Anirban DasGupta Pdf

This unique book delivers an encyclopedic treatment of classic as well as contemporary large sample theory, dealing with both statistical problems and probabilistic issues and tools. The book is unique in its detailed coverage of fundamental topics. 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. 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.

Author : Lucien Le Cam,Grace Lo Yang
Publisher : Springer Science & Business Media
Page : 189 pages
File Size : 50,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468403770

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Asymptotics in Statistics by Lucien Le Cam,Grace Lo Yang Pdf

In the summer of 1968 one of the present authors (LLC) had the pleasure of giving a sequence of lectures at the University of Mon treal. Lecture notes were collected and written out by Drs. Catherine Doleans, Jean Haezendonck and Roch Roy. They were published in French by the Presses of the University of Montreal as part of their series of Seminaires de Mathematiques Superieures. Twenty years later it was decided that a Chinese translation could be useful, but upon prodding by Professor Shanti Gupta at Purdue we concluded that the notes should be updated and rewritten in English and in Chinese. The present volume is the result of that effort. We have preserved the general outline of the lecture notes, but we have deleted obsolete material and sketched some of the results acquired during the past twenty years. This means that while the original notes concentrated on the LAN situation we have included here some results of Jeganathan and others on the LAMN case. Also included are versions of the Hajek-Le Cam asymptotic minimax and convolution theorems with some of their implications. We have not attempted to give complete coverage of the subject and have often stated theorems without indicating their proofs.

Author : Anirban DasGupta
Publisher : Springer Science & Business Media
Page : 727 pages
File Size : 54,5 Mb
Release : 2008-02-06
Category : Mathematics
ISBN : 9780387759715

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Asymptotic Theory of Statistics and Probability by Anirban DasGupta Pdf

This unique book delivers an encyclopedic treatment of classic as well as contemporary large sample theory, dealing with both statistical problems and probabilistic issues and tools. The book is unique in its detailed coverage of fundamental topics. 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. 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.

Author : A. W. van der Vaart
Publisher : Cambridge University Press
Page : 128 pages
File Size : 48,9 Mb
Release : 2000-06-19
Category : Mathematics
ISBN : 9781107268449

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Asymptotic Statistics by A. W. van der Vaart Pdf

This book is an introduction to the field of asymptotic statistics. The treatment is both practical and mathematically rigorous. In addition to most of the standard topics of an asymptotics course, including likelihood inference, M-estimation, the theory of asymptotic efficiency, U-statistics, and rank procedures, the book also presents recent research topics such as semiparametric models, the bootstrap, and empirical processes and their applications. The topics are organized from the central idea of approximation by limit experiments, which gives the book one of its unifying themes. This entails mainly the local approximation of the classical i.i.d. set up with smooth parameters by location experiments involving a single, normally distributed observation. Thus, even the standard subjects of asymptotic statistics are presented in a novel way. Suitable as a graduate or Master's level statistics text, this book will also give researchers an overview of research in asymptotic statistics.

Author : Madan L. Puri
Publisher : Walter de Gruyter GmbH & Co KG
Page : 456 pages
File Size : 50,5 Mb
Release : 2018-11-05
Category : Mathematics
ISBN : 9783110942002

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Asymptotics in Statistics and Probability by Madan L. Puri Pdf

No detailed description available for "Asymptotics in Statistics and Probability".

Author : D.R. Cox
Publisher : Routledge
Page : 275 pages
File Size : 47,9 Mb
Release : 2017-10-19
Category : Mathematics
ISBN : 9781351438551

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Inference and Asymptotics by D.R. Cox Pdf

Our book Asymptotic Techniquesfor Use in Statistics was originally planned as an account of asymptotic statistical theory, but by the time we had completed the mathematical preliminaries it seemed best to publish these separately. The present book, although largely self-contained, takes up the original theme and gives a systematic account of some recent developments in asymptotic parametric inference from a likelihood-based perspective. Chapters 1-4 are relatively elementary and provide first a review of key concepts such as likelihood, sufficiency, conditionality, ancillarity, exponential families and transformation models. Then first-order asymptotic theory is set out, followed by a discussion of the need for higher-order theory. This is then developed in some generality in Chapters 5-8. A final chapter deals briefly with some more specialized issues. The discussion emphasizes concepts and techniques rather than precise mathematical verifications with full attention to regularity conditions and, especially in the less technical chapters, draws quite heavily on illustrative examples. Each chapter ends with outline further results and exercises and with bibliographic notes. Many parts of the field discussed in this book are undergoing rapid further development, and in those parts the book therefore in some respects has more the flavour of a progress report than an exposition of a largely completed theory.

Author : T. L. Lai,Lianfen Qian,Qi-Man Shao
Publisher : Unknown
Page : 560 pages
File Size : 49,6 Mb
Release : 2008
Category : Mathematics
ISBN : UOM:39015080827655

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Asymptotic Theory in Probability and Statistics with Applications by T. L. Lai,Lianfen Qian,Qi-Man Shao Pdf

Presents a collection of 18 papers, many of which are surveys, on asymptotic theory in probability and statistics, with applications to a variety of problems. This volume comprises three parts: limit theorems, statistics and applications, and mathematical finance and insurance. It is suitable for graduate students in probability and statistics.

Author : N. Balakrishnan,I.A.V.B. Ibragimov,V.B. Nevzorov
Publisher : Springer Science & Business Media
Page : 541 pages
File Size : 48,9 Mb
Release : 2012-12-06
Category : Business & Economics
ISBN : 9781461202097

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Asymptotic Methods in Probability and Statistics with Applications by N. Balakrishnan,I.A.V.B. Ibragimov,V.B. Nevzorov Pdf

Traditions of the 150-year-old St. Petersburg School of Probability and Statis tics had been developed by many prominent scientists including P. L. Cheby chev, A. M. Lyapunov, A. A. Markov, S. N. Bernstein, and Yu. V. Linnik. In 1948, the Chair of Probability and Statistics was established at the Department of Mathematics and Mechanics of the St. Petersburg State University with Yu. V. Linik being its founder and also the first Chair. Nowadays, alumni of this Chair are spread around Russia, Lithuania, France, Germany, Sweden, China, the United States, and Canada. The fiftieth anniversary of this Chair was celebrated by an International Conference, which was held in St. Petersburg from June 24-28, 1998. More than 125 probabilists and statisticians from 18 countries (Azerbaijan, Canada, Finland, France, Germany, Hungary, Israel, Italy, Lithuania, The Netherlands, Norway, Poland, Russia, Taiwan, Turkey, Ukraine, Uzbekistan, and the United States) participated in this International Conference in order to discuss the current state and perspectives of Probability and Mathematical Statistics. The conference was organized jointly by St. Petersburg State University, St. Petersburg branch of Mathematical Institute, and the Euler Institute, and was partially sponsored by the Russian Foundation of Basic Researches. The main theme of the Conference was chosen in the tradition of the St.

Author : Christopher G. Small
Publisher : CRC Press
Page : 357 pages
File Size : 43,7 Mb
Release : 2010-05-07
Category : Mathematics
ISBN : 1420011022

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Expansions and Asymptotics for Statistics by Christopher G. Small Pdf

Asymptotic methods provide important tools for approximating and analysing functions that arise in probability and statistics. Moreover, the conclusions of asymptotic analysis often supplement the conclusions obtained by numerical methods. Providing a broad toolkit of analytical methods, Expansions and Asymptotics for Statistics shows how asymptotics, when coupled with numerical methods, becomes a powerful way to acquire a deeper understanding of the techniques used in probability and statistics. The book first discusses the role of expansions and asymptotics in statistics, the basic properties of power series and asymptotic series, and the study of rational approximations to functions. With a focus on asymptotic normality and asymptotic efficiency of standard estimators, it covers various applications, such as the use of the delta method for bias reduction, variance stabilisation, and the construction of normalising transformations, as well as the standard theory derived from the work of R.A. Fisher, H. Cramér, L. Le Cam, and others. The book then examines the close connection between saddle-point approximation and the Laplace method. The final chapter explores series convergence and the acceleration of that convergence.

Author : B. L. S. Prakasa Rao
Publisher : Unknown
Page : 458 pages
File Size : 53,8 Mb
Release : 1987-01-16
Category : Mathematics
ISBN : UOM:39015046271048

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Asymptotic Theory of Statistical Inference by B. L. S. Prakasa Rao Pdf

Probability and stochastic processes; Limit theorems for some statistics; Asymptotic theory of estimation; Linear parametric inference; Martingale approach to inference; Inference in nonlinear regression; Von mises functionals; Empirical characteristic function and its applications.

Author : D.R. Cox,O.E. Barndorff-Nielsen
Publisher : CRC Press
Page : 376 pages
File Size : 51,5 Mb
Release : 1994-03-01
Category : Mathematics
ISBN : 041249440X

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Inference and Asymptotics by D.R. Cox,O.E. Barndorff-Nielsen Pdf

Likelihood and its many associated concepts are of central importance in statistical theory and applications. The theory of likelihood and of likelihood-like objects (pseudo-likelihoods) has undergone extensive and important developments over the past 10 to 15 years, in particular as regards higher order asymptotics. This book provides an account of this field, which is still vigorously expanding. Conditioning and ancillarity underlie the p*-formula, a key formula for the conditional density of the maximum likelihood estimator, given an ancillary statistic. Various types of pseudo-likelihood are discussed, including profile and partial likelihoods. Special emphasis is given to modified profile likelihood and modified directed likelihood, and their intimate connection with the p*-formula. Among the other concepts and tools employed are sufficiency, parameter orthogonality, invariance, stochastic expansions and saddlepoint approximations. Brief reviews are given of the most important properties of exponential and transformation models and these types of model are used as test-beds for the general asymptotic theory. A final chapter briefly discusses a number of more general issues, including prediction and randomization theory. The emphasis is on ideas and methods, and detailed mathematical developments are largely omitted. There are numerous notes and exercises, many indicating substantial further results.

Author : Jana Jurecková,Pranab Kumar Sen
Publisher : John Wiley & Sons
Page : 496 pages
File Size : 45,7 Mb
Release : 1996-04-19
Category : Mathematics
ISBN : 0471822213

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Robust Statistical Procedures by Jana Jurecková,Pranab Kumar Sen Pdf

A broad and unified methodology for robust statistics—with exciting new applications Robust statistics is one of the fastest growing fields in contemporary statistics. It is also one of the more diverse and sometimes confounding areas, given the many different assessments and interpretations of robustness by theoretical and applied statisticians. This innovative book unifies the many varied, yet related, concepts of robust statistics under a sound theoretical modulation. It seamlessly integrates asymptotics and interrelations, and provides statisticians with an effective system for dealing with the interrelations between the various classes of procedures. Drawing on the expertise of researchers from around the world, and covering over a decade's worth of developments in the field, Robust Statistical Procedures: Asymptotics and Interrelations: Discusses both theory and applications in its two parts, from the fundamentals to robust statistical inference Thoroughly explores the interrelations between diverse classes of procedures, unlike any other book Compares nonparametric procedures with robust statistics, explaining in detail asymptotic representations for various estimators Provides a timesaving list of mathematical tools for the problems under discussion Keeps mathematical abstractions to a minimum, in spite of its largely theoretical content Includes useful problems and exercises at the end of each chapter Offers strategies for more complex models when using robust statistical procedures Self-contained and rounded in approach, this book is invaluable for both applied statisticians and theoretical researchers; for graduate students in mathematical statistics; and for anyone interested in the influence of this methodology.

Author : J. K. Ghosh
Publisher : IMS
Page : 126 pages
File Size : 52,9 Mb
Release : 1994
Category : Mathematics
ISBN : 0940600315

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Higher Order Asymptotics by J. K. Ghosh Pdf

Author : D.R. Cox
Publisher : Routledge
Page : 360 pages
File Size : 50,6 Mb
Release : 2017-10-19
Category : Mathematics
ISBN : 9781351438568

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Inference and Asymptotics by D.R. Cox Pdf

Our book Asymptotic Techniquesfor Use in Statistics was originally planned as an account of asymptotic statistical theory, but by the time we had completed the mathematical preliminaries it seemed best to publish these separately. The present book, although largely self-contained, takes up the original theme and gives a systematic account of some recent developments in asymptotic parametric inference from a likelihood-based perspective. Chapters 1-4 are relatively elementary and provide first a review of key concepts such as likelihood, sufficiency, conditionality, ancillarity, exponential families and transformation models. Then first-order asymptotic theory is set out, followed by a discussion of the need for higher-order theory. This is then developed in some generality in Chapters 5-8. A final chapter deals briefly with some more specialized issues. The discussion emphasizes concepts and techniques rather than precise mathematical verifications with full attention to regularity conditions and, especially in the less technical chapters, draws quite heavily on illustrative examples. Each chapter ends with outline further results and exercises and with bibliographic notes. Many parts of the field discussed in this book are undergoing rapid further development, and in those parts the book therefore in some respects has more the flavour of a progress report than an exposition of a largely completed theory.

Author : Gauri Sankar Datta,Rahul Mukerjee
Publisher : Springer Science & Business Media
Page : 138 pages
File Size : 43,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461220367

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Probability Matching Priors: Higher Order Asymptotics by Gauri Sankar Datta,Rahul Mukerjee Pdf

This is the first book on the topic of probability matching priors. It targets researchers, Bayesian and frequentist; graduate students in Statistics.