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Author : John McKinley Chambers
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (769 download)
Download or read book Some Methods of Asymptotic Approximation in Multivariate Statistical Analysis written by John McKinley Chambers and published by . This book was released on 1966 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Yasunori Fujikoshi
Publisher : Springer Nature
ISBN 13 : 9811326169
Total Pages : 133 pages
Book Rating : 4.8/5 (113 download)
Download or read book Non-Asymptotic Analysis of Approximations for Multivariate Statistics written by Yasunori Fujikoshi and published by Springer Nature. This book was released on 2020-06-28 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents recent non-asymptotic results for approximations in multivariate statistical analysis. The book is unique in its focus on results with the correct error structure for all the parameters involved. Firstly, it discusses the computable error bounds on correlation coefficients, MANOVA tests and discriminant functions studied in recent papers. It then introduces new areas of research in high-dimensional approximations for bootstrap procedures, Cornish–Fisher expansions, power-divergence statistics and approximations of statistics based on observations with random sample size. Lastly, it proposes a general approach for the construction of non-asymptotic bounds, providing relevant examples for several complicated statistics. It is a valuable resource for researchers with a basic understanding of multivariate statistics.
Author : Karl W. Breitung
Publisher : Springer
ISBN 13 : 3540490337
Total Pages : 157 pages
Book Rating : 4.5/5 (44 download)
Download or read book Asymptotic Approximations for Probability Integrals written by Karl W. Breitung and published by Springer. This book was released on 2006-11-14 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a self-contained introduction to the subject of asymptotic approximation for multivariate integrals for both mathematicians and applied scientists. A collection of results of the Laplace methods is given. Such methods are useful for example in reliability, statistics, theoretical physics and information theory. An important special case is the approximation of multidimensional normal integrals. Here the relation between the differential geometry of the boundary of the integration domain and the asymptotic probability content is derived. One of the most important applications of these methods is in structural reliability. Engineers working in this field will find here a complete outline of asymptotic approximation methods for failure probability integrals.
Author : Subir Ghosh
Publisher : CRC Press
ISBN 13 : 9780824700515
Total Pages : 864 pages
Book Rating : 4.7/5 (5 download)
Download or read book Asymptotics, Nonparametrics, and Time Series written by Subir Ghosh and published by CRC Press. This book was released on 1999-02-18 with total page 864 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Contains over 2500 equations and exhaustively covers not only nonparametrics but also parametric, semiparametric, frequentist, Bayesian, bootstrap, adaptive, univariate, and multivariate statistical methods, as well as practical uses of Markov chain models."
Author : Yasunori Fujikoshi
Publisher : John Wiley & Sons
ISBN 13 : 0470539860
Total Pages : 564 pages
Book Rating : 4.4/5 (75 download)
Download or read book Multivariate Statistics written by Yasunori Fujikoshi and published by John Wiley & Sons. This book was released on 2011-08-15 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive examination of high-dimensional analysis of multivariate methods and their real-world applications Multivariate Statistics: High-Dimensional and Large-Sample Approximations is the first book of its kind to explore how classical multivariate methods can be revised and used in place of conventional statistical tools. Written by prominent researchers in the field, the book focuses on high-dimensional and large-scale approximations and details the many basic multivariate methods used to achieve high levels of accuracy. The authors begin with a fundamental presentation of the basic tools and exact distributional results of multivariate statistics, and, in addition, the derivations of most distributional results are provided. Statistical methods for high-dimensional data, such as curve data, spectra, images, and DNA microarrays, are discussed. Bootstrap approximations from a methodological point of view, theoretical accuracies in MANOVA tests, and model selection criteria are also presented. Subsequent chapters feature additional topical coverage including: High-dimensional approximations of various statistics High-dimensional statistical methods Approximations with computable error bound Selection of variables based on model selection approach Statistics with error bounds and their appearance in discriminant analysis, growth curve models, generalized linear models, profile analysis, and multiple comparison Each chapter provides real-world applications and thorough analyses of the real data. In addition, approximation formulas found throughout the book are a useful tool for both practical and theoretical statisticians, and basic results on exact distributions in multivariate analysis are included in a comprehensive, yet accessible, format. Multivariate Statistics is an excellent book for courses on probability theory in statistics at the graduate level. It is also an essential reference for both practical and theoretical statisticians who are interested in multivariate analysis and who would benefit from learning the applications of analytical probabilistic methods in statistics.
Author : Risto D.H. Heijmans
Publisher : Springer Science & Business Media
ISBN 13 : 1461546036
Total Pages : 302 pages
Book Rating : 4.4/5 (615 download)
Download or read book Innovations in Multivariate Statistical Analysis written by Risto D.H. Heijmans and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: The three decades which have followed the publication of Heinz Neudecker's seminal paper `Some Theorems on Matrix Differentiation with Special Reference to Kronecker Products' in the Journal of the American Statistical Association (1969) have witnessed the growing influence of matrix analysis in many scientific disciplines. Amongst these are the disciplines to which Neudecker has contributed directly - namely econometrics, economics, psychometrics and multivariate analysis. This book aims to illustrate how powerful the tools of matrix analysis have become as weapons in the statistician's armoury. The majority of its chapters are concerned primarily with theoretical innovations, but all of them have applications in view, and some of them contain extensive illustrations of the applied techniques. This book will provide research workers and graduate students with a cross-section of innovative work in the fields of matrix methods and multivariate statistical analysis. It should be of interest to students and practitioners in a wide range of subjects which rely upon modern methods of statistical analysis. The contributors to the book are themselves practitioners of a wide range of subjects including econometrics, psychometrics, educational statistics, computation methods and electrical engineering, but they find a common ground in the methods which are represented in the book. It is envisaged that the book will serve as an important work of reference and as a source of inspiration for some years to come.
Author : Wolfgang Karl Härdle
Publisher : Springer Science & Business Media
ISBN 13 : 3662058022
Total Pages : 480 pages
Book Rating : 4.6/5 (62 download)
Download or read book Applied Multivariate Statistical Analysis written by Wolfgang Karl Härdle and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: A state of the art presentation of the tools and concepts of multivariate data analysis with a strong focus on applications. The first part is devoted to graphical techniques describing the distributions of the involved variables. The second part deals with multivariate random variables and presents distributions, estimators and tests for various practical situations. The last part covers mulivariate techniques and introduces the reader into the wide variety of tools for multivariate data analysis. The text presents a wide range of examples and 228 exercises.
Author : Christopher A. Field
Publisher : IMS
ISBN 13 : 9780940600188
Total Pages : 166 pages
Book Rating : 4.6/5 (1 download)
Download or read book Small Sample Asymptotics written by Christopher A. Field and published by IMS. This book was released on 1990 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Masanobu Taniguchi
Publisher : Springer Science & Business Media
ISBN 13 : 146123154X
Total Pages : 169 pages
Book Rating : 4.4/5 (612 download)
Download or read book Higher Order Asymptotic Theory for Time Series Analysis written by Masanobu Taniguchi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: The initial basis of this book was a series of my research papers, that I listed in References. I have many people to thank for the book's existence. Regarding higher order asymptotic efficiency I thank Professors Kei Takeuchi and M. Akahira for their many comments. I used their concept of efficiency for time series analysis. During the summer of 1983, I had an opportunity to visit The Australian National University, and could elucidate the third-order asymptotics of some estimators. I express my sincere thanks to Professor E.J. Hannan for his warmest encouragement and kindness. Multivariate time series analysis seems an important topic. In 1986 I visited Center for Mul tivariate Analysis, University of Pittsburgh. I received a lot of impact from multivariate analysis, and applied many multivariate methods to the higher order asymptotic theory of vector time series. I am very grateful to the late Professor P.R. Krishnaiah for his cooperation and kindness. In Japan my research was mainly performed in Hiroshima University. There is a research group of statisticians who are interested in the asymptotic expansions in statistics. Throughout this book I often used the asymptotic expansion techniques. I thank all the members of this group, especially Professors Y. Fujikoshi and K. Maekawa foItheir helpful discussion. When I was a student of Osaka University I learned multivariate analysis and time series analysis from Professors Masashi Okamoto and T. Nagai, respectively. It is a pleasure to thank them for giving me much of research background.
Author : O. E. Barndorff-Nielsen
Publisher : Springer
ISBN 13 :
Total Pages : 272 pages
Book Rating : 4.:/5 (319 download)
Download or read book Asymptotic Techniques for Use in Statistics written by O. E. Barndorff-Nielsen and published by Springer. This book was released on 1989-03 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Olga Dunajeva
Publisher : LAP Lambert Academic Publishing
ISBN 13 : 9783846599822
Total Pages : 104 pages
Book Rating : 4.5/5 (998 download)
Download or read book Asymtotic Matrix Methods written by Olga Dunajeva and published by LAP Lambert Academic Publishing. This book was released on 2011-12 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: The exact distributions of multivariate statistics used for the inference in multivariate analysis are usually not known or quite difficult to handle. The topic of this book belongs to the area of approximation of unknown distributions through classical distributions and to the related estimation problems. The methods used here are based on concepts of matrix algebra like the Kronecker product, the vec-operator and the matrix derivative. The multivariate normal distribution and the class of elliptical distributions are examined. The asymptotic variance of the sample correlation coefficient is calculated using approximate linearization. Some applications of the asymptotic distribution of the sample correlation coefficient are considered for populations with different distributions. The main term of the bias of the shape parameter of the asymmetric normal distribution and the Lauter's F-statistic was found using the Taylor expansion. Simulation experiments are described and the results of the simulation study are presented beside derivation of theoretical results.
Author : Karl Wilhelm Breitung
Publisher : Springer Verlag
ISBN 13 : 9780387586175
Total Pages : 146 pages
Book Rating : 4.5/5 (861 download)
Download or read book Asymptotic Approximations for Probability Integrals written by Karl Wilhelm Breitung and published by Springer Verlag. This book was released on 1994-01-01 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a self-contained introduction to the subject of asymptotic approximation for multivariate integrals for both mathematicians and applied scientists. A collection of results of the Laplace methods is given. Such methods are useful for example in reliability, statistics, theoretical physics and information theory. An important special case is the approximation of multidimensional normal integrals. Here the relation between the differential geometry of the boundary of the integration domain and the asymptotic probability content is derived. One of the most important applications of these methods is in structural reliability. Engineers working in this field will find here a complete outline of asymptotic approximation methods for failure probability integrals.
Author : John E. Kolassa
Publisher : Springer Science & Business Media
ISBN 13 : 1475742770
Total Pages : 194 pages
Book Rating : 4.4/5 (757 download)
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 194 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 sub ject, 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 on 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.
Author : Rabi N. Bhattacharya
Publisher : SIAM
ISBN 13 : 089871897X
Total Pages : 333 pages
Book Rating : 4.8/5 (987 download)
Download or read book Normal Approximation and Asymptotic Expansions written by Rabi N. Bhattacharya and published by SIAM. This book was released on 2010-11-11 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: -Fourier analysis, --
Author : Lucien Le Cam
Publisher : Springer Science & Business Media
ISBN 13 : 1461249465
Total Pages : 767 pages
Book Rating : 4.4/5 (612 download)
Download or read book Asymptotic Methods in Statistical Decision Theory written by Lucien Le Cam and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 767 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : James Dickson Murray
Publisher : Oxford University Press, USA
ISBN 13 :
Total Pages : 152 pages
Book Rating : 4.:/5 (319 download)
Download or read book Asymptotic Analysis written by James Dickson Murray and published by Oxford University Press, USA. This book was released on 1974 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "A good introduction to a subject important for its capacity to circumvent theoretical and practical obstacles, and therefore particularly prized in the applications of mathematics. The book presents a balanced view of the methods and their usefulness: integrals on the real line and in the complex plane which arise in different contexts, and solutions of differential equations not expressible as integrals. Murray includes both historical remarks and references to sources or other more complete treatments. More useful as a guide for self-study than as a reference work, it is accessible to any upperclass mathematics undergraduate. Some exercises and a short bibliography included. Even with E.T. Copson's "Asymptotic" "Expansions" or N.G. de Bruijn's "Asymptotic Methods in" "Analysis" (1958), any academic library would do well to have this excellent introduction." ("S. Puckette, University of" "the South") #"Choice Sept. 1984"#1
Author : Pranab K. Sen
Publisher : Cambridge University Press
ISBN 13 : 0521877229
Total Pages : 399 pages
Book Rating : 4.5/5 (218 download)
Download or read book From Finite Sample to Asymptotic Methods in Statistics written by Pranab K. Sen and published by Cambridge University Press. This book was released on 2010 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: A broad view of exact statistical inference and the development of asymptotic statistical inference.
