Elements of modern asymptotic theory with statistical applications

by Brendan McCabe

Publisher: Manchester University Press, Publisher: Distributed exclusively in the USA and Canada by St. Martin"s Press in Manchester [England], New York, New York

Written in English
Cover of: Elements of modern asymptotic theory with statistical applications | Brendan McCabe
Published: Pages: 264 Downloads: 284
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Subjects:

  • Statistical hypothesis testing -- Asymptotic theory.,
  • Estimation theory -- Asymptotic theory.

Edition Notes

Includes bibliographical references (p. [255]-256) and index.

StatementBrendan McCabe and Andrew Tremayne.
ContributionsTremayne, Andrew, 1947-
Classifications
LC ClassificationsQA277 .M39 1993
The Physical Object
Paginationxi, 264 p. :
Number of Pages264
ID Numbers
Open LibraryOL1727343M
ISBN 100719030528, 0719030536
LC Control Number92031520

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: Elements of Modern Asymptotic Theory With Statistical Applications (): McCabe, Brendan, Tremayne, Andrew: BooksCited by: Elements of Modern Asymptotic Theory with Statistical Applications Elements of Modern Asymptotic Theory with Statistical Applications, Andrew Tremayne: Authors: Brendan McCabe, Andrew Tremayne: Edition: illustrated: Publisher: Manchester University Press, ISBN:Length: pages: Subjects.

Elements of modern asymptotic theory with statistical applications. Elements of modern asymptotic theory with statistical applications book [England] ; New York: Manchester University Press ; New York: Distributed exclusively in the USA and Canada by St.

Martin's Press, © For most applications of asymptotic theory to statistical problems, the objects of interest are sequences of random vectors (or matrices), say X N or Y N; which are typically statistics indexed by the sample size N; the object is to –nd simple approximations for the distribution functions of X N or Y N.

Review of "Elements of Modern Asymptotic Theory with Statistical Applications" [Review of: B. McCabe, A. Tremayne () Elements of Modern Asymptotic Theory with Statistical Applications] Published in: Econometric Reviews, 17(3), - Taylor and Francis Ltd.

ISSN Author: Boswijk, H.P. Publisher: ASE RI (FEB) Date issued: Cited by: 3. Part of the attraction of this book is its pleasant, straightforward style of exposition, leavened with a touch of humor and occasionally even using the dramatic form of dialogue. The book begins with a general introduction (fundamental to the whole book) on O and o notation and asymptotic series in s: 9.

This is a reprinting of a book originally published in At that time it was the first book on the subject of homogenization, which is the asymptotic analysis of partial differential equations with rapidly oscillating coefficients, and as such it sets the stage for what problems to consider and what methods to use, including probabilistic s: 3.

The primary purpose of this paper is to review a very few results on some basic elements of large sample theory in a restricted structural framework, as described in detail in the recent book by LeCam and Yang (, Asymptotics in Statistics: Some Basic Concepts.

New York: Springer), and to illustrate how the asymptotic inference problems. of statistical theory and methodology; (iii) to provide exposure to key ideas in contemporary statistical theory; and (iv) to provide practice in application of key techniques to particular problems.

References •Barndorff-Nielsen, O.E. and Cox, D.R. ()Asymptotic Techniques for Use in Statistics. Linking astronomy to the world of modern statistics, this volume is a unique resource, introducing astronomers to advanced statistics through ready-to-use code in the public domain R statistical software environment.

The book presents fundamental results of probability theory and statistical inference, before exploring several fields of applied Reviews: 4. The asymptotic distributions of the test statistics are nonnormal.

The associated tests are shown to have good power against a wide range of alternatives. One also exhibits the application of the tests to a number of statistical hypothesis testing problems, some of which seemingly bear no relationship to tests for constancy of a mean.

The book makes accessible to students and practicing professionals in statistics, general mathematics, operations research, and engineering the essentials of: * The tools and foundations that are basic to asymptotic theory in statistics * The asymptotics of statistics computed from a sample, including transformations of vectors of more basic.

Downloadable. The primary purpose of this paper is to review a very few results on some basic elements of large sample theory in a restricted structural framework, as described in detail in the recent book by LeCam and Yang (, Asymptotics in Statistics: Some Basic Concepts.

New York: Springer), and to illustrate how the asymptotic inference problems associated with a wide variety of time. Asymptotic theory is the single most unifying theme of probability and statistics.

Particularly, in statistics, nearly every method or rule or tradition has its root in some result in asymptotic theory. No other branch of probability and statistics has such an incredibly rich body of literature, tools, and applications, in amazingly diverse.

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.

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 autoregressive (AR), moving average (MA), and autoregressive moving average (ARMA) processes.

Among these are the fantastic and concise A Course in Large Sample Theory by Thomas Ferguson, the comprehensive and beautifully written Asymptotic Statistics by A. van der Vaart, and the classic probability textbooks Probability and Measure by Patrick Billingsley and An Introduction to Probability Theory and Its Applications, Volumes 1 and 2.

The key assumptions to obtain the asymptotic unbiasedness include that the candidate models are good approximation to the true DGP, the consistency and asymptotic normality of MLE, and the expression for the asymptotic variance of MLE.

For details, see Li et al. (a). This book is intended to provide a somewhat more comprehensive and unified treatment of large sample theory than has been available previously and to relate the fundamental tools of asymptotic theory directly to many of the estimators of interest to econometricians.

An up-to-date and concise description of recent results in probability theory and stochastic processes useful in the study of asymptotic theory of statistical inference. Brings together new material on the interplay between recent advances in probability theory and their applications to the asymptotic theory of statistical inference.

McCabe, B. and A. Tremayne () Elements of Modern Asymptotic Theory with Statistical Applications, Manchester: Manchester University Press. Mills, T. () Time Series Techniques for Economists.

Cambridge: Cambridge University Press Ouliaris, S. and P. Phillips () COINT Gauss Procedures for Cointegrated. Informed throughout by real-world applications, the book includes topics such as the Fokker-Planck equation, boundary layer analysis, WKB approximation, applications of spectral theory, as well as recent results in narrow escape theory.

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. In statistics: asymptotic theory, or large sample theory, is a framework for assessing properties of estimators and statistical this framework, it is often assumed that the sample size n may grow indefinitely; the properties of estimators and tests are then evaluated under the limit of n → ∞.In practice, a limit evaluation is considered to be approximately valid for large.

Mathématiques & applications, Edition/Format: Print book: FrenchView all editions and formats: Rating: (not yet rated) 0 with reviews - Be the first.

Subjects: Mathematical statistics -- Asymptotic theory. Statistique mathématique -- Théorie asymptotique. Asymptotische Statistik; View all subjects; More like this: Similar Items. Objectives of Asymptotic Theory While exact results are available for, say, the distribution of the classical least squares estimator for the normal linear regression model, and for other leading special combinations of distributions and statistics, generally distributional results are unavailable when statistics are nonlinear in the underlying.

Asymptotic theory plays a fundamental role in the developments of modern statistics, especially in the theoretical analysis of new methodologies.

Some asymptotic results may borrow directly from the limit theory in probability, but many need deep insights of statistical contents and more accurate approximations, which have in turn fostered.

The authors present a rigorous account of the concepts and a broad treatment of the major results of classical finite sample size decision theory and modern asymptotic decision theory. Highlights are systematic applications to the fields of parameter estimation, testing hypotheses, and.

Econometrics is statistical analysis of economic and nancial data. It has become an integral part of training in modern economics and business. This book develops a coherent set of econometric theory and methods for economic models.

A timely and applied approach to the newly discovered methods and applications of U-statistics Built on years of collaborative research and academic experience, Modern Applied U-Statistics successfully presents a thorough introduction to the theory of U-statistics using in-depth examples and applications that address contemporary areas of study including biomedical and.

Asymptotic theory is a central unifying theme to both theoretical and applied statistics. This theory underlies much of the work on different topics such as maximum likelihood estimation, likelihood ratio tests and some of their variants, the bootstrap, etc.

Teachers and young research students of mathematical statistics need to have a proper background of the various results related to.Notes on asymptotic methods in statistical decision theory.

Montreal: Centre de Recherches Mathématiques, Université de Montréal, (OCoLC) Material Type: Government publication, National government publication: Document Type: Book: All Authors / .Probability, Statistics and Econometrics provides a concise, yet rigorous, treatment of the field that is suitable for graduate students studying econometrics, very advanced undergraduate students, and researchers seeking to extend their knowledge of the trinity of fields that use quantitative data in economic decision-making.

The book covers much of the groundwork for probability and.