Series Approximation Methods In Statistics
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Series Approximation Methods In Statistics
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Author : John Edward Kolassa
language : en
Publisher: Springer Science & Business Media
Release Date : 1994
Series Approximation Methods In Statistics written by John Edward Kolassa and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
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
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Author : John E. Kolassa
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Series Approximation Methods In Statistics written by John E. Kolassa and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
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.
Normal Approximation
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Author : Vladimir V. Senatov
language : en
Publisher: Walter de Gruyter
Release Date : 2011-09-08
Normal Approximation written by Vladimir V. Senatov and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-08 with Mathematics categories.
The series is devoted to the publication of high-level monographs and surveys which cover the whole spectrum of probability and statistics. The books of the series are addressed to both experts and advanced students.
Multivariate Statistics
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Author : Yasunori Fujikoshi
language : en
Publisher: John Wiley & Sons
Release Date : 2011-08-15
Multivariate Statistics written by Yasunori Fujikoshi and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-15 with Mathematics categories.
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.
Real Time Analytics
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Author : Byron Ellis
language : en
Publisher: John Wiley & Sons
Release Date : 2014-06-23
Real Time Analytics written by Byron Ellis and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-23 with Computers categories.
Construct a robust end-to-end solution for analyzing and visualizing streaming data Real-time analytics is the hottest topic in data analytics today. In Real-Time Analytics: Techniques to Analyze and Visualize Streaming Data, expert Byron Ellis teaches data analysts technologies to build an effective real-time analytics platform. This platform can then be used to make sense of the constantly changing data that is beginning to outpace traditional batch-based analysis platforms. The author is among a very few leading experts in the field. He has a prestigious background in research, development, analytics, real-time visualization, and Big Data streaming and is uniquely qualified to help you explore this revolutionary field. Moving from a description of the overall analytic architecture of real-time analytics to using specific tools to obtain targeted results, Real-Time Analytics leverages open source and modern commercial tools to construct robust, efficient systems that can provide real-time analysis in a cost-effective manner. The book includes: A deep discussion of streaming data systems and architectures Instructions for analyzing, storing, and delivering streaming data Tips on aggregating data and working with sets Information on data warehousing options and techniques Real-Time Analytics includes in-depth case studies for website analytics, Big Data, visualizing streaming and mobile data, and mining and visualizing operational data flows. The book's "recipe" layout lets readers quickly learn and implement different techniques. All of the code examples presented in the book, along with their related data sets, are available on the companion website.
Approximation Theorems Of Mathematical Statistics
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Author : Robert J. Serfling
language : en
Publisher: Wiley-Interscience
Release Date : 1980-12-08
Approximation Theorems Of Mathematical Statistics written by Robert J. Serfling and has been published by Wiley-Interscience this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980-12-08 with Mathematics categories.
Approximation Theorems of Mathematical Statistics This convenient paperback edition makes a seminal text in statistics accessible to a new generation of students and practitioners. Approximation Theorems of Mathematical Statistics covers a broad range of limit theorems useful in mathematical statistics, along with methods of proof and techniques of application. The manipulation of "probability" theorems to obtain "statistical" theorems is emphasized. Besides a knowledge of these basic statistical theorems, this lucid introduction to the subject imparts an appreciation of the instrumental role of probability theory. 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 statistics, with emphasis on asymptotic distribution theory and strong convergence * Important special classes of statistics, such as maximum likelihood estimates and other asymptotic efficient procedures; W. Hoeffding's U-statistics and R. von Mises's "differentiable statistical functions" * Statistics obtained as solutions of equations ("M-estimates"), linear functions of order statistics ("L-statistics"), and rank statistics ("R-statistics") * Use of influence curves * Approaches toward asymptotic relative efficiency of statistical test procedures
Time Series Theory And Methods
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Author : Peter J. Brockwell
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Time Series Theory And Methods written by Peter J. Brockwell and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.
We have attempted in this book to give a systematic account of linear time series models and their application to the modelling and prediction of data collected sequentially in time. The aim is to provide specific techniques for handling data and at the same time to provide a thorough understanding of the mathematical basis for the techniques. Both time and frequency domain methods are discussed but the book is written in such a way that either approach could be emphasized. The book is intended to be a text for graduate students in statistics, mathematics, engineering, and the natural or social sciences. It has been used both at the M. S. level, emphasizing the more practical aspects of modelling, and at the Ph. D. level, where the detailed mathematical derivations of the deeper results can be included. Distinctive features of the book are the extensive use of elementary Hilbert space methods and recursive prediction techniques based on innovations, use of the exact Gaussian likelihood and AIC for inference, a thorough treatment of the asymptotic behavior of the maximum likelihood estimators of the coefficients of univariate ARMA models, extensive illustrations of the tech niques by means of numerical examples, and a large number of problems for the reader. The companion diskette contains programs written for the IBM PC, which can be used to apply the methods described in the text.
Approximation Methods In Probability Theory
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Author : Vydas Čekanavičius
language : en
Publisher: Springer
Release Date : 2016-06-16
Approximation Methods In Probability Theory written by Vydas Čekanavičius and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-16 with Mathematics categories.
This book presents a wide range of well-known and less common methods used for estimating the accuracy of probabilistic approximations, including the Esseen type inversion formulas, the Stein method as well as the methods of convolutions and triangle function. Emphasising the correct usage of the methods presented, each step required for the proofs is examined in detail. As a result, this textbook provides valuable tools for proving approximation theorems. While Approximation Methods in Probability Theory will appeal to everyone interested in limit theorems of probability theory, the book is particularly aimed at graduate students who have completed a standard intermediate course in probability theory. Furthermore, experienced researchers wanting to enlarge their toolkit will also find this book useful.
Quantitative Approximations
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Author : George Anastassiou
language : en
Publisher: CRC Press
Release Date : 2000-09-15
Quantitative Approximations written by George Anastassiou and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-09-15 with Mathematics categories.
Quantitative approximation methods apply in many diverse fields of research-neural networks, wavelets, partial differential equations, probability and statistics, functional analysis, and classical analysis to name just a few. For the first time in book form, Quantitative Approximations provides a thorough account of all of the significant developments in the area of contemporary quantitative mathematics. It offers readers the unique opportunity of approaching the field under the guidance of an expert. Among the book's outstanding features is the inclusion of the introductory chapter that summarizes the primary and most useful results. This section serves not only as a more detailed table of contents for those new to an area of application, but also as a quick reference for more seasoned researchers. The author describes all of the pertinent mathematical entities precisely and concretely. His approach and proofs are straightforward and constructive, making Quantitative Approximations accessible and valuable to researchers and graduate students alike.
Approximation Theory And Algorithms For Data Analysis
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Author : Armin Iske
language : en
Publisher: Springer
Release Date : 2018-12-14
Approximation Theory And Algorithms For Data Analysis written by Armin Iske and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-14 with Mathematics categories.
This textbook offers an accessible introduction to the theory and numerics of approximation methods, combining classical topics of approximation with recent advances in mathematical signal processing, and adopting a constructive approach, in which the development of numerical algorithms for data analysis plays an important role. The following topics are covered: * least-squares approximation and regularization methods * interpolation by algebraic and trigonometric polynomials * basic results on best approximations * Euclidean approximation * Chebyshev approximation * asymptotic concepts: error estimates and convergence rates * signal approximation by Fourier and wavelet methods * kernel-based multivariate approximation * approximation methods in computerized tomography Providing numerous supporting examples, graphical illustrations, and carefully selected exercises, this textbook is suitable for introductory courses, seminars, and distance learning programs on approximation for undergraduate students.