Series Approximation Methods in Statistics

Series Approximation Methods in Statistics

Author: John Edward Kolassa

Publisher: Springer Science & Business Media

Published: 1994

Total Pages: 150

ISBN-13: 9780387942773

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Asymptotic techniques have long been important in statistical inference; these techniques remain important in the age of fast computing because some exact answers are still either conceptually unavailable or practically out of reach. This book presents theoretical results relevant to Edgeworth and saddlepoint expansions to densities and distribution functions. It provides examples of their application in some simple, and in a few complicated, settings. Numerical and asymptotic assessments of accuracy are presented. Variants of these expansions, including much of modern likelihood theory, are discussed. Applications to lattice distributions are extensively treated.


Book Synopsis Series Approximation Methods in Statistics by : John Edward Kolassa

Download or read book Series Approximation Methods in Statistics written by John Edward Kolassa and published by Springer Science & Business Media. This book was released on 1994 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotic techniques have long been important in statistical inference; these techniques remain important in the age of fast computing because some exact answers are still either conceptually unavailable or practically out of reach. This book presents theoretical results relevant to Edgeworth and saddlepoint expansions to densities and distribution functions. It provides examples of their application in some simple, and in a few complicated, settings. Numerical and asymptotic assessments of accuracy are presented. Variants of these expansions, including much of modern likelihood theory, are discussed. Applications to lattice distributions are extensively treated.

Series Approximation Methods in Statistics

Series Approximation Methods in Statistics

Author: John E. Kolassa

Publisher:

Published: 2014-01-15

Total Pages: 164

ISBN-13: 9781475742763

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Book Synopsis Series Approximation Methods in Statistics by : John E. Kolassa

Download or read book Series Approximation Methods in Statistics written by John E. Kolassa and published by . This book was released on 2014-01-15 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Series Approximation Methods in Statistics

Series Approximation Methods in Statistics

Author: John E. Kolassa

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 162

ISBN-13: 1475742754

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This book was originally compiled for a course I taught at the University of Rochester in the fall of 1991, and is intended to give advanced graduate students in statistics an introduction to Edgeworth and saddlepoint approximations, and related techniques. Many other authors have also written monographs on this subject, and so this work is narrowly focused on two areas not recently discussed in theoretical text books. These areas are, first, a rigorous consideration of Edgeworth and saddlepoint expansion limit theorems, and second, a survey of the more recent developments in the field. In presenting expansion limit theorems I have drawn heavily 011 notation of McCullagh (1987) and on the theorems presented by Feller (1971) on Edgeworth expansions. For saddlepoint notation and results I relied most heavily on the many papers of Daniels, and a review paper by Reid (1988). Throughout this book I have tried to maintain consistent notation and to present theorems in such a way as to make a few theoretical results useful in as many contexts as possible. This was not only in order to present as many results with as few proofs as possible, but more importantly to show the interconnections between the various facets of asymptotic theory. Special attention is paid to regularity conditions. The reasons they are needed and the parts they play in the proofs are both highlighted.


Book Synopsis Series Approximation Methods in Statistics by : John E. Kolassa

Download or read book Series Approximation Methods in Statistics written by John E. Kolassa and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book was originally compiled for a course I taught at the University of Rochester in the fall of 1991, and is intended to give advanced graduate students in statistics an introduction to Edgeworth and saddlepoint approximations, and related techniques. Many other authors have also written monographs on this subject, and so this work is narrowly focused on two areas not recently discussed in theoretical text books. These areas are, first, a rigorous consideration of Edgeworth and saddlepoint expansion limit theorems, and second, a survey of the more recent developments in the field. In presenting expansion limit theorems I have drawn heavily 011 notation of McCullagh (1987) and on the theorems presented by Feller (1971) on Edgeworth expansions. For saddlepoint notation and results I relied most heavily on the many papers of Daniels, and a review paper by Reid (1988). Throughout this book I have tried to maintain consistent notation and to present theorems in such a way as to make a few theoretical results useful in as many contexts as possible. This was not only in order to present as many results with as few proofs as possible, but more importantly to show the interconnections between the various facets of asymptotic theory. Special attention is paid to regularity conditions. The reasons they are needed and the parts they play in the proofs are both highlighted.

Approximation Methods in Statistics

Approximation Methods in Statistics

Author: P. Whittle

Publisher:

Published: 1980

Total Pages:

ISBN-13:

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Book Synopsis Approximation Methods in Statistics by : P. Whittle

Download or read book Approximation Methods in Statistics written by P. Whittle and published by . This book was released on 1980 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Approximate Distributions of Order Statistics

Approximate Distributions of Order Statistics

Author: Rolf-Dieter Reiss

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 363

ISBN-13: 1461396204

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This book is designed as a unified and mathematically rigorous treatment of some recent developments of the asymptotic distribution theory of order statistics (including the extreme order statistics) that are relevant for statistical theory and its applications. Particular emphasis is placed on results concern ing the accuracy oflimit theorems, on higher order approximations, and other approximations in quite a general sense. Contrary to the classical limit theorems that primarily concern the weak convergence of distribution functions, our main results will be formulated in terms of the variational and the Hellinger distance. These results will form the proper springboard for the investigation of parametric approximations of nonparametric models of joint distributions of order statistics. The approxi mating models include normal as well as extreme value models. Several applications will show the usefulness of this approach. Other recent developments in statistics like nonparametric curve estima tion and the bootstrap method will be studied as far as order statistics are concerned. 1n connection with this, graphical methods will, to some extent, be explored.


Book Synopsis Approximate Distributions of Order Statistics by : Rolf-Dieter Reiss

Download or read book Approximate Distributions of Order Statistics written by Rolf-Dieter Reiss and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is designed as a unified and mathematically rigorous treatment of some recent developments of the asymptotic distribution theory of order statistics (including the extreme order statistics) that are relevant for statistical theory and its applications. Particular emphasis is placed on results concern ing the accuracy oflimit theorems, on higher order approximations, and other approximations in quite a general sense. Contrary to the classical limit theorems that primarily concern the weak convergence of distribution functions, our main results will be formulated in terms of the variational and the Hellinger distance. These results will form the proper springboard for the investigation of parametric approximations of nonparametric models of joint distributions of order statistics. The approxi mating models include normal as well as extreme value models. Several applications will show the usefulness of this approach. Other recent developments in statistics like nonparametric curve estima tion and the bootstrap method will be studied as far as order statistics are concerned. 1n connection with this, graphical methods will, to some extent, be explored.

Tensor Methods in Statistics

Tensor Methods in Statistics

Author: Peter McCullagh

Publisher: Courier Dover Publications

Published: 2018-07-18

Total Pages: 308

ISBN-13: 0486832694

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A pioneering monograph on tensor methods applied to distributional problems arising in statistics, this work begins with the study of multivariate moments and cumulants. An invaluable reference for graduate students and professional statisticians. 1987 edition.


Book Synopsis Tensor Methods in Statistics by : Peter McCullagh

Download or read book Tensor Methods in Statistics written by Peter McCullagh and published by Courier Dover Publications. This book was released on 2018-07-18 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: A pioneering monograph on tensor methods applied to distributional problems arising in statistics, this work begins with the study of multivariate moments and cumulants. An invaluable reference for graduate students and professional statisticians. 1987 edition.

Saddlepoint Approximation Methods in the Analysis of Panel Time Series Data

Saddlepoint Approximation Methods in the Analysis of Panel Time Series Data

Author: Devindri Perera

Publisher:

Published: 2007

Total Pages: 448

ISBN-13:

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Book Synopsis Saddlepoint Approximation Methods in the Analysis of Panel Time Series Data by : Devindri Perera

Download or read book Saddlepoint Approximation Methods in the Analysis of Panel Time Series Data written by Devindri Perera and published by . This book was released on 2007 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Normal Approximation by Stein’s Method

Normal Approximation by Stein’s Method

Author: Louis H.Y. Chen

Publisher: Springer Science & Business Media

Published: 2010-10-13

Total Pages: 411

ISBN-13: 3642150071

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Since its introduction in 1972, Stein’s method has offered a completely novel way of evaluating the quality of normal approximations. Through its characterizing equation approach, it is able to provide approximation error bounds in a wide variety of situations, even in the presence of complicated dependence. Use of the method thus opens the door to the analysis of random phenomena arising in areas including statistics, physics, and molecular biology. Though Stein's method for normal approximation is now mature, the literature has so far lacked a complete self contained treatment. This volume contains thorough coverage of the method’s fundamentals, includes a large number of recent developments in both theory and applications, and will help accelerate the appreciation, understanding, and use of Stein's method by providing the reader with the tools needed to apply it in new situations. It addresses researchers as well as graduate students in Probability, Statistics and Combinatorics.


Book Synopsis Normal Approximation by Stein’s Method by : Louis H.Y. Chen

Download or read book Normal Approximation by Stein’s Method written by Louis H.Y. Chen and published by Springer Science & Business Media. This book was released on 2010-10-13 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since its introduction in 1972, Stein’s method has offered a completely novel way of evaluating the quality of normal approximations. Through its characterizing equation approach, it is able to provide approximation error bounds in a wide variety of situations, even in the presence of complicated dependence. Use of the method thus opens the door to the analysis of random phenomena arising in areas including statistics, physics, and molecular biology. Though Stein's method for normal approximation is now mature, the literature has so far lacked a complete self contained treatment. This volume contains thorough coverage of the method’s fundamentals, includes a large number of recent developments in both theory and applications, and will help accelerate the appreciation, understanding, and use of Stein's method by providing the reader with the tools needed to apply it in new situations. It addresses researchers as well as graduate students in Probability, Statistics and Combinatorics.

Statistical Methods

Statistical Methods

Author: Rudolf J. Freund

Publisher: Elsevier

Published: 2003-01-07

Total Pages: 694

ISBN-13: 0080498221

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This broad text provides a complete overview of most standard statistical methods, including multiple regression, analysis of variance, experimental design, and sampling techniques. Assuming a background of only two years of high school algebra, this book teaches intelligent data analysis and covers the principles of good data collection. * Provides a complete discussion of analysis of data including estimation, diagnostics, and remedial actions * Examples contain graphical illustration for ease of interpretation * Intended for use with almost any statistical software * Examples are worked to a logical conclusion, including interpretation of results * A complete Instructor's Manual is available to adopters


Book Synopsis Statistical Methods by : Rudolf J. Freund

Download or read book Statistical Methods written by Rudolf J. Freund and published by Elsevier. This book was released on 2003-01-07 with total page 694 pages. Available in PDF, EPUB and Kindle. Book excerpt: This broad text provides a complete overview of most standard statistical methods, including multiple regression, analysis of variance, experimental design, and sampling techniques. Assuming a background of only two years of high school algebra, this book teaches intelligent data analysis and covers the principles of good data collection. * Provides a complete discussion of analysis of data including estimation, diagnostics, and remedial actions * Examples contain graphical illustration for ease of interpretation * Intended for use with almost any statistical software * Examples are worked to a logical conclusion, including interpretation of results * A complete Instructor's Manual is available to adopters

Approximation Theorems of Mathematical Statistics

Approximation Theorems of Mathematical Statistics

Author: R. J. Serfling

Publisher:

Published: 1980

Total Pages: 371

ISBN-13: 9780471137306

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Book Synopsis Approximation Theorems of Mathematical Statistics by : R. J. Serfling

Download or read book Approximation Theorems of Mathematical Statistics written by R. J. Serfling and published by . This book was released on 1980 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: