Download or read book Non Asymptotic Analysis of Approximations for Multivariate Statistics written by Yasunori Fujikoshi and published by . This book was released on 2020 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.

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.

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.

Download or read book Stability Problems for Stochastic Models Theory and Applications written by Alexander Zeifman and published by MDPI. This book was released on 2021-03-05 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this Special Issue of Mathematics is to commemorate the outstanding Russian mathematician Vladimir Zolotarev, whose 90th birthday will be celebrated on February 27th, 2021. The present Special Issue contains a collection of new papers by participants in sessions of the International Seminar on Stability Problems for Stochastic Models founded by Zolotarev. Along with research in probability distributions theory, limit theorems of probability theory, stochastic processes, mathematical statistics, and queuing theory, this collection contains papers dealing with applications of stochastic models in modeling of pension schemes, modeling of extreme precipitation, construction of statistical indicators of scientific publication importance, and other fields.

Download or read book An Author and Permuted Title Index to Selected Statistical Journals written by Brian L. Joiner and published by . This book was released on 1970 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: All articles, notes, queries, corrigenda, and obituaries appearing in the following journals during the indicated years are indexed: Annals of mathematical statistics, 1961-1969; Biometrics, 1965-1969#3; Biometrics, 1951-1969; Journal of the American Statistical Association, 1956-1969; Journal of the Royal Statistical Society, Series B, 1954-1969,#2; South African statistical journal, 1967-1969,#2; Technometrics, 1959-1969.--p.iv.

Download or read book Multiparametric Statistics written by Vadim Ivanovich Serdobolskii and published by Elsevier. This book was released on 2007-10-18 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents mathematical theory of statistical models described by the essentially large number of unknown parameters, comparable with sample size but can also be much larger. In this meaning, the proposed theory can be called "essentially multiparametric". It is developed on the basis of the Kolmogorov asymptotic approach in which sample size increases along with the number of unknown parameters.This theory opens a way for solution of central problems of multivariate statistics, which up until now have not been solved. Traditional statistical methods based on the idea of an infinite sampling often break down in the solution of real problems, and, dependent on data, can be inefficient, unstable and even not applicable. In this situation, practical statisticians are forced to use various heuristic methods in the hope the will find a satisfactory solution.Mathematical theory developed in this book presents a regular technique for implementing new, more efficient versions of statistical procedures. Near exact solutions are constructed for a number of concrete multi-dimensional problems: estimation of expectation vectors, regression and discriminant analysis, and for the solution to large systems of empiric linear algebraic equations. It is remarkable that these solutions prove to be not only non-degenerating and always stable, but also near exact within a wide class of populations.In the conventional situation of small dimension and large sample size these new solutions far surpass the classical, commonly used consistent ones. It can be expected in the near future, for the most part, traditional multivariate statistical software will be replaced by the always reliable and more efficient versions of statistical procedures implemented by the technology described in this book.This monograph will be of interest to a variety of specialists working with the theory of statistical methods and its applications. Mathematicians would find new classes of urgent problems to be solved in their own regions. Specialists in applied statistics creating statistical packages will be interested in more efficient methods proposed in the book. Advantages of these methods are obvious: the user is liberated from the permanent uncertainty of possible instability and inefficiency and gets algorithms with unimprovable accuracy and guaranteed for a wide class of distributions.A large community of specialists applying statistical methods to real data will find a number of always stable highly accurate versions of algorithms that will help them to better solve their scientific or economic problems. Students and postgraduates will be interested in this book as it will help them get at the foremost frontier of modern statistical science. - Presents original mathematical investigations and open a new branch of mathematical statistics- Illustrates a technique for developing always stable and efficient versions of multivariate statistical analysis for large-dimensional problems - Describes the most popular methods some near exact solutions; including algorithms of non-degenerating large-dimensional discriminant and regression analysis

Download or read book NBS Special Publication written by and published by . This book was released on 1970 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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."

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:

Download or read book Saddlepoint Approximations with Applications written by Ronald W. Butler and published by Cambridge University Press. This book was released on 2007-08-16 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern statistical methods use complex, sophisticated models that can lead to intractable computations. Saddlepoint approximations can be the answer. Written from the user's point of view, this book explains in clear language how such approximate probability computations are made, taking readers from the very beginnings to current applications. The core material is presented in chapters 1-6 at an elementary mathematical level. Chapters 7-9 then give a highly readable account of higher-order asymptotic inference. Later chapters address areas where saddlepoint methods have had substantial impact: multivariate testing, stochastic systems and applied probability, bootstrap implementation in the transform domain, and Bayesian computation and inference. No previous background in the area is required. Data examples from real applications demonstrate the practical value of the methods. Ideal for graduate students and researchers in statistics, biostatistics, electrical engineering, econometrics, and applied mathematics, this is both an entry-level text and a valuable reference.

Download or read book Normal Approximation and Asymptotic Expansions written by Rabindra Nath Bhattacharya and published by . This book was released on 1986 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Advances in Multivariate Statistical Analysis written by Arjun K. Gupta and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: The death of Professor K.C. Sreedharan Pillai on June 5, 1985 was a heavy loss to many statisticians all around the world. This volume is dedicated to his memory in recog nition of his many contributions in multivariate statis tical analysis. It brings together eminent statisticians Working in multivariate analysis from around the world. The research and expository papers cover a cross-section of recent developments in the field. This volume is especially useful to researchers and to those who want to keep abreast of the latest directions in multivariate statistical analysis. I am grateful to the authors from so many different countries and research institutions who contributed to this volume. I wish to express my appreciation to all those who have reviewed the papers. The list of people include Professors T.C. Chang, So-Hsiang Chou, Dipak K. Dey, Peter Hall, Yu-Sheng Hsu, J.D. Knoke, W.J. Krzanowski, Edsel Pena, Bimal K. Sinha, Dennis L. Young, Drs. K. Krishnamoorthy, D.K. Nagar, and Messrs. Alphonse Amey, Chi-Chin Chao and Samuel Ofori-Nyarko. I wish to thank Professors Shanti S. Gupta and James 0. Berger for their keen interest and encouragement. Thanks are also due to Cynthia Patterson for her help and Reidel Publishing Com~any for their cooperation in bringing this volume out.

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, --

Download or read book Multivariate Statistical Analysis written by Mukhopadhyay Parimal and published by World Scientific Publishing Company. This book was released on 2008-11-25 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook presents a classical approach to some techniques of multivariate analysis in a simple and transparent manner. It offers clear and concise development of the concepts; interpretation of the output of the analysis; and criteria for selection of the methods, taking into account the strengths and weaknesses of each. With its roots in matrix algebra, for which a separate chapter has been added as an appendix, the book includes both data-oriented techniques and a reasonable coverage of classical methods supplemented by comments about robustness and general practical applicability. It also illustrates the methods of numerical calculations at various stages.This self-contained book is ideal as an advanced textbook for graduate students in statistics and other disciplines like social, biological and physical sciences. It will also be of benefit to professional statisticians.The author is a former Professor of the Indian Statistical Institute, India.

Download or read book Modern Directional Statistics written by Christophe Ley and published by CRC Press. This book was released on 2017-08-03 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern Directional Statistics collects important advances in methodology and theory for directional statistics over the last two decades. It provides a detailed overview and analysis of recent results that can help both researchers and practitioners. Knowledge of multivariate statistics eases the reading but is not mandatory. The field of directional statistics has received a lot of attention over the past two decades, due to new demands from domains such as life sciences or machine learning, to the availability of massive data sets requiring adapted statistical techniques, and to technological advances. This book covers important progresses in distribution theory,high-dimensional statistics, kernel density estimation, efficient inference on directional supports, and computational and graphical methods. Christophe Ley is professor of mathematical statistics at Ghent University. His research interests include semi-parametrically efficient inference, flexible modeling, directional statistics and the study of asymptotic approximations via Stein’s Method. His achievements include the Marie-Jeanne Laurent-Duhamel prize of the Société Française de Statistique and an elected membership at the International Statistical Institute. He is associate editor for the journals Computational Statistics & Data Analysis and Econometrics and Statistics. Thomas Verdebout is professor of mathematical statistics at Université libre de Bruxelles (ULB). His main research interests are semi-parametric statistics, high- dimensional statistics, directional statistics and rank-based procedures. He has won an annual prize of the Belgian Academy of Sciences and is an elected member of the International Statistical Institute. He is associate editor for the journals Statistics and Probability Letters and Journal of Multivariate Analysis.

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.

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.