Asymptotic Statistics

Author : A. W. van der Vaart
Publisher : Cambridge University Press
Page : 470 pages
File Size : 53,9 Mb
Release : 2000-06-19
Category : Mathematics
ISBN : 0521784506

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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 the latest research in asymptotic statistics.

Author : Anirban DasGupta
Publisher : Springer Science & Business Media
Page : 726 pages
File Size : 51,7 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 : Lucien Le Cam,Grace Lo Yang
Publisher : Springer Science & Business Media
Page : 299 pages
File Size : 44,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461211662

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

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.

Author : Lucien Le Cam
Publisher : Springer Science & Business Media
Page : 767 pages
File Size : 55,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461249467

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Asymptotic Methods in Statistical Decision Theory by Lucien Le Cam Pdf

This book grew out of lectures delivered at the University of California, Berkeley, over many years. The subject is a part of asymptotics in statistics, organized around a few central ideas. The presentation proceeds from the general to the particular since this seemed the best way to emphasize the basic concepts. The reader is expected to have been exposed to statistical thinking and methodology, as expounded for instance in the book by H. Cramer [1946] or the more recent text by P. Bickel and K. Doksum [1977]. Another pos sibility, closer to the present in spirit, is Ferguson [1967]. Otherwise the reader is expected to possess some mathematical maturity, but not really a great deal of detailed mathematical knowledge. Very few mathematical objects are used; their assumed properties are simple; the results are almost always immediate consequences of the definitions. Some objects, such as vector lattices, may not have been included in the standard background of a student of statistics. For these we have provided a summary of relevant facts in the Appendix. The basic structures in the whole affair are systems that Blackwell called "experiments" and "transitions" between them. An "experiment" is a mathe matical abstraction intended to describe the basic features of an observational process if that process is contemplated in advance of its implementation. Typically, an experiment consists of a set E> of theories about what may happen in the observational process.

Author : Reinhard Höpfner
Publisher : Walter de Gruyter GmbH & Co KG
Page : 286 pages
File Size : 52,5 Mb
Release : 2014-05-26
Category : Mathematics
ISBN : 9783110367782

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Asymptotic Statistics by Reinhard Höpfner Pdf

This textbook is devoted to the general asymptotic theory of statistical experiments. Local asymptotics for statistical models in the sense of local asymptotic (mixed) normality or local asymptotic quadraticity make up the core of the book. Numerous examples deal with classical independent and identically distributed models and with stochastic processes. The book can be read in different ways, according to possibly different mathematical preferences of the reader. One reader may focus on the statistical theory, and thus on the chapters about Gaussian shift models, mixed normal and quadratic models, and on local asymptotics where the limit model is a Gaussian shift or a mixed normal or a quadratic experiment (LAN, LAMN, LAQ). Another reader may prefer an introduction to stochastic process models where given statistical results apply, and thus concentrate on subsections or chapters on likelihood ratio processes and some diffusion type models where LAN, LAMN or LAQ occurs. Finally, readers might put together both aspects. The book is suitable for graduate students starting to work in statistics of stochastic processes, as well as for researchers interested in a precise introduction to this area.

Author : Helmut Rieder
Publisher : Springer Science & Business Media
Page : 409 pages
File Size : 43,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468406245

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Robust Asymptotic Statistics by Helmut Rieder Pdf

1 To the king, my lord, from your servant Balasi : 2 ... The king should have a look. Maybe the scribe who reads to the king did not understand . . . . shall I personally show, with this tablet that I am sending to the king, my lord, how the omen was written. 3 Really, he who has not followed the text with his finger cannot possibly understand it. This book is about optimally robust functionals and their unbiased esti mators and tests. Functionals extend the parameter of the assumed ideal center model to neighborhoods of this model that contain the actual distri bution. The two principal questions are (F): Which functional to choose? and (P): Which statistical procedure to use for the selected functional? Using a local asymptotic framework, we deal with both problems by linking up nonparametric statistical optimality with infinitesimal robust ness criteria. Thus, seemingly separate developments in robust statistics are presented in a unifying way.

Author : Martin J. Wainwright
Publisher : Cambridge University Press
Page : 571 pages
File Size : 49,5 Mb
Release : 2019-02-21
Category : Business & Economics
ISBN : 9781108498029

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High-Dimensional Statistics by Martin J. Wainwright Pdf

A coherent introductory text from a groundbreaking researcher, focusing on clarity and motivation to build intuition and understanding.

Author : Masanobu Taniguchi,Yoshihide Kakizawa
Publisher : Springer Science & Business Media
Page : 671 pages
File Size : 41,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461211624

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Asymptotic Theory of Statistical Inference for Time Series by Masanobu Taniguchi,Yoshihide Kakizawa Pdf

The primary aim of this book is to provide modern statistical techniques and theory for stochastic processes. The stochastic processes mentioned here are not restricted to the usual AR, MA, and ARMA processes. A wide variety of stochastic processes, including non-Gaussian linear processes, long-memory processes, nonlinear processes, non-ergodic processes and diffusion processes are described. The authors discuss estimation and testing theory and many other relevant statistical methods and techniques.

Author : Aleksandr Petrovich Korostelev,Olga Korosteleva
Publisher : American Mathematical Soc.
Page : 258 pages
File Size : 47,5 Mb
Release : 2011
Category : Asymptotic efficiencies (Statistics).
ISBN : 9780821852835

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Mathematical Statistics by Aleksandr Petrovich Korostelev,Olga Korosteleva Pdf

iPositive Give a man a fish, he eats for a day, but if you teach him to fish, you feed him for life. Such is the approach of iPositive. One day at the gym doesnt make a person fit for life; its a consistent dedication to getting the body in shape that eventually yields results. The lessons in iPositive work in much the same way: They challenge the reader to work to keep the mind in shape. The book is a powerful guide to personal happiness through positivity. Its concepts provide empowerment to overcome self-doubt, disbelief and inferiority complexes in order to transcend the negativity in life. iPositive is geared toward helping individuals become more focused on the things they most want in life, like happiness, love and success, or banish anchors that may be weighting them down, like stress, smoking or excess weight. The book gives readers the practical means to become more focused on those things they want in life, and serves as an inspirational manual for a life of fulfillment, and strength in body, mind and spirit.

Author : Manfred Denker,Rabi Bhattacharya
Publisher : Birkhäuser
Page : 121 pages
File Size : 49,6 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 : Anirban DasGupta
Publisher : Springer Science & Business Media
Page : 727 pages
File Size : 52,6 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 : J. Pfanzagl
Publisher : Springer Science & Business Media
Page : 324 pages
File Size : 44,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461257691

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Contributions to a General Asymptotic Statistical Theory by J. Pfanzagl Pdf

Author : I.A. Ibragimov,R.Z. Has'minskii
Publisher : Springer Science & Business Media
Page : 410 pages
File Size : 49,5 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781489900272

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Statistical Estimation by I.A. Ibragimov,R.Z. Has'minskii Pdf

when certain parameters in the problem tend to limiting values (for example, when the sample size increases indefinitely, the intensity of the noise ap proaches zero, etc.) To address the problem of asymptotically optimal estimators consider the following important case. Let X 1, X 2, ... , X n be independent observations with the joint probability density !(x,O) (with respect to the Lebesgue measure on the real line) which depends on the unknown patameter o e 9 c R1. It is required to derive the best (asymptotically) estimator 0:( X b ... , X n) of the parameter O. The first question which arises in connection with this problem is how to compare different estimators or, equivalently, how to assess their quality, in terms of the mean square deviation from the parameter or perhaps in some other way. The presently accepted approach to this problem, resulting from A. Wald's contributions, is as follows: introduce a nonnegative function w(0l> ( ), Ob Oe 9 (the loss function) and given two estimators Of and O! n 2 2 the estimator for which the expected loss (risk) Eown(Oj, 0), j = 1 or 2, is smallest is called the better with respect to Wn at point 0 (here EoO is the expectation evaluated under the assumption that the true value of the parameter is 0). Obviously, such a method of comparison is not without its defects.

Author : Reinhard Höpfner
Publisher : Walter de Gruyter
Page : 286 pages
File Size : 42,9 Mb
Release : 2014-01-31
Category : Mathematics
ISBN : 9783110250282

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Asymptotic Statistics by Reinhard Höpfner Pdf

This textbook is devoted to the general asymptotic theory of statistical experiments. Local asymptotics for statistical models in the sense of local asymptotic (mixed) normality or local asymptotic quadraticity make up the core of the book. Numerous examples deal with classical independent and identically distributed models and with stochastic processes. The book can be read in different ways, according to possibly different mathematical preferences of the reader. One reader may focus on the statistical theory, and thus on the chapters about Gaussian shift models, mixed normal and quadratic models, and on local asymptotics where the limit model is a Gaussian shift or a mixed normal or a quadratic experiment (LAN, LAMN, LAQ). Another reader may prefer an introduction to stochastic process models where given statistical results apply, and thus concentrate on subsections or chapters on likelihood ratio processes and some diffusion type models where LAN, LAMN or LAQ occurs. Finally, readers might put together both aspects. The book is suitable for graduate students starting to work in statistics of stochastic processes, as well as for researchers interested in a precise introduction to this area.

Author : Petr Mandl,Marie Huskova
Publisher : Springer Science & Business Media
Page : 463 pages
File Size : 40,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642579844

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Asymptotic Statistics by Petr Mandl,Marie Huskova Pdf

In particular up-to-date-information is presented in detection of systematic changes, in series of observation, in robust regression analysis, in numerical empirical processes and in related areas of actuarial sciences.