Expansions And Asymptotics For Statistics

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 : Johann Pfanzagl
Publisher : Unknown
Page : 520 pages
File Size : 54,5 Mb
Release : 2014-09-01
Category : Electronic
ISBN : 1461564808

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Asymptotic Expansions for General Statistical Models by Johann Pfanzagl Pdf

Author : J. K. Ghosh
Publisher : IMS
Page : 126 pages
File Size : 46,5 Mb
Release : 1994
Category : Mathematics
ISBN : 0940600315

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Higher Order Asymptotics by J. K. Ghosh Pdf

Author : Manfred Denker,Rabi Bhattacharya
Publisher : Birkhäuser
Page : 121 pages
File Size : 53,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783034892544

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Asymptotic Statistics by Manfred Denker,Rabi Bhattacharya Pdf

These notes are based on lectures presented during the seminar on " Asymptotic Statistics" held at SchloB Reisensburg, Gunzburg, May 29-June 5, 1988. They consist of two parts, the theory of asymptotic expansions in statistics and probabilistic aspects of the asymptotic distribution theory in nonparametric statistics. Our intention is to provide a comprehensive presentation of these two subjects, leading from elementary facts to the advanced theory and recent results. Prospects for further research are also included. We would like to thank all participants for their stimulating discussions and their interest in the subjects, which made lecturing very pleasant. Special thanks are due H. Zimmer for her excellent typing. We would also like to take this opportunity to to express our thanks to the Gesellschaft fur mathematische Forschung and to the Deutsche Mathematiker Vereinigung, especially to Professor G. Fischer, for the opportunity to present these lectures and to the Birkhauser Verlag for the publication of these lecture notes. R. Bhattacharya, M. Denker Part I: Asymptotic Expansions in Statistics Rabi Bhattacharya 11 {sect}1. CRAMER-EDGEWORTH EXPANSIONS Let Q be a probability measure on (IRk, B"), B" denoting the Borel sigmafield on IR". Assume that the s - th absolute moment of Q is finite, (1.1) P. := J II x lis Q(dx)

Author : Lucien Le Cam,Grace Lo Yang
Publisher : Springer Science & Business Media
Page : 189 pages
File Size : 43,5 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 : Rabi N. Bhattacharya,R. Ranga Rao
Publisher : SIAM
Page : 333 pages
File Size : 51,7 Mb
Release : 2010-11-11
Category : Mathematics
ISBN : 9780898718973

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Normal Approximation and Asymptotic Expansions by Rabi N. Bhattacharya,R. Ranga Rao Pdf

-Fourier analysis, --

Author : Christopher A. Field,Elvezio Ronchetti
Publisher : IMS
Page : 166 pages
File Size : 50,7 Mb
Release : 1990
Category : Mathematical statistics
ISBN : 0940600188

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Small Sample Asymptotics by Christopher A. Field,Elvezio Ronchetti Pdf

Author : A. W. van der Vaart
Publisher : Cambridge University Press
Page : 128 pages
File Size : 53,8 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 : Vladimir E. Bening
Publisher : Walter de Gruyter
Page : 305 pages
File Size : 46,8 Mb
Release : 2011-08-30
Category : Mathematics
ISBN : 9783110935998

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Asymptotic Theory of Testing Statistical Hypotheses by Vladimir E. Bening Pdf

The series is devoted to the publication of high-level monographs and surveys which cover the whole spectrum of probability and statistics. The books of the series are addressed to both experts and advanced students.

Author : Anirban DasGupta
Publisher : Springer Science & Business Media
Page : 726 pages
File Size : 50,7 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 : N. Balakrishnan,I.A.V.B. Ibragimov,V.B. Nevzorov
Publisher : Springer Science & Business Media
Page : 541 pages
File Size : 52,9 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 : O. E. Barndorff-Nielsen,D. R. Cox
Publisher : Springer
Page : 272 pages
File Size : 43,7 Mb
Release : 1989-03
Category : Mathematics
ISBN : MINN:319510004572896

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Asymptotic Techniques for Use in Statistics by O. E. Barndorff-Nielsen,D. R. Cox Pdf

The use in statistical theory of approximate arguments based on such methods as local linearization (the delta method) and approxi mate normality has a long history. Such ideas play at least three roles. First they may give simple approximate answers to distributional problems where an exact solution is known in principle but difficult to implement. The second role is to yield higher-order expansions from which the accuracy of simple approximations may be assessed and where necessary improved. Thirdly the systematic development of a theoretical approach to statistical inference that will apply to quite general families of statistical models demands an asymptotic formulation, as far as possible one that will recover 'exact' results where these are available. The approximate arguments are developed by supposing that some defining quantity, often a sample size but more generally an amount of information, becomes large: it must be stressed that this is a technical device for generating approximations whose adequacy always needs assessing, rather than a 'physical' limiting notion. Of the three roles outlined above, the first two are quite close to the traditional roles of asymptotic expansions in applied mathematics and much ofthe very extensive literature on the asymptotic expansion of integrals and of the special functions of mathematical physics is quite directly relevant, although the recasting of these methods into a probability mould is quite often enlightening.

Author : Rabindra Nath Bhattacharya
Publisher : Unknown
Page : 316 pages
File Size : 52,6 Mb
Release : 1986
Category : Asymptotic expansions
ISBN : 0898719895

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Normal Approximation and Asymptotic Expansions by Rabindra Nath Bhattacharya Pdf

Although this was first published in 1976, it has gained new significance and renewed interest among statisticians due to the developments of modern statistical techniques such as the bootstrap, the efficacy of which can be ascertained by asymptotic expansions. This also is the only book containing a detailed treatment of various refinements of the multivariate central limit theorem (CLT), including Berry-Essen-type error bounds for probabilities of general classes of functions and sets, and asymptotic expansions for both lattice and non-lattice distributions.

Author : Peter K. Friz,Jim Gatheral,Archil Gulisashvili,Antoine Jacquier,Josef Teichmann
Publisher : Springer
Page : 590 pages
File Size : 46,7 Mb
Release : 2015-06-16
Category : Mathematics
ISBN : 9783319116051

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Large Deviations and Asymptotic Methods in Finance by Peter K. Friz,Jim Gatheral,Archil Gulisashvili,Antoine Jacquier,Josef Teichmann Pdf

Topics covered in this volume (large deviations, differential geometry, asymptotic expansions, central limit theorems) give a full picture of the current advances in the application of asymptotic methods in mathematical finance, and thereby provide rigorous solutions to important mathematical and financial issues, such as implied volatility asymptotics, local volatility extrapolation, systemic risk and volatility estimation. This volume gathers together ground-breaking results in this field by some of its leading experts. Over the past decade, asymptotic methods have played an increasingly important role in the study of the behaviour of (financial) models. These methods provide a useful alternative to numerical methods in settings where the latter may lose accuracy (in extremes such as small and large strikes, and small maturities), and lead to a clearer understanding of the behaviour of models, and of the influence of parameters on this behaviour. Graduate students, researchers and practitioners will find this book very useful, and the diversity of topics will appeal to people from mathematical finance, probability theory and differential geometry.

Author : Ricardo Estrada,Ram P. Kanwal
Publisher : Springer Science & Business Media
Page : 467 pages
File Size : 42,5 Mb
Release : 2012-09-08
Category : Mathematics
ISBN : 9780817681302

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A Distributional Approach to Asymptotics by Ricardo Estrada,Ram P. Kanwal Pdf

"...The authors of this remarkable book are among the very few who have faced up to the challenge of explaining what an asymptotic expansion is, and of systematizing the handling of asymptotic series. The idea of using distributions is an original one, and we recommend that you read the book...[it] should be on your bookshelf if you are at all interested in knowing what an asymptotic series is." -"The Bulletin of Mathematics Books" (Review of the 1st edition) ** "...The book is a valuable one, one that many applied mathematicians may want to buy. The authors are undeniably experts in their field...most of the material has appeared in no other book." -"SIAM News" (Review of the 1st edition) This book is a modern introduction to asymptotic analysis intended not only for mathematicians, but for physicists, engineers, and graduate students as well. Written by two of the leading experts in the field, the text provides readers with a firm grasp of mathematical theory, and at the same time demonstrates applications in areas such as differential equations, quantum mechanics, noncommutative geometry, and number theory. Key features of this significantly expanded and revised second edition: * addition of a new chapter and many new sections * wide range of topics covered, including the Ces.ro behavior of distributions and their connections to asymptotic analysis, the study of time-domain asymptotics, and the use of series of Dirac delta functions to solve boundary value problems * novel approach detailing the interplay between underlying theories of asymptotic analysis and generalized functions * extensive examples and exercises at the end of each chapter * comprehensive bibliography and index This work is an excellent tool for the classroom and an invaluable self-study resource that will stimulate application of asymptotic