The Bootstrap and Edgeworth Expansion


Author: Peter Hall
Publisher: Springer Science & Business Media
ISBN: 146124384X
Category: Mathematics
Page: 354
View: 5821

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This monograph addresses two quite different topics, each being able to shed light on the other. Firstly, it lays the foundation for a particular view of the bootstrap. Secondly, it gives an account of Edgeworth expansion. The first two chapters deal with the bootstrap and Edgeworth expansion respectively, while chapters 3 and 4 bring these two themes together, using Edgeworth expansion to explore and develop the properties of the bootstrap. The book is aimed at graduate level for those with some exposure to the methods of theoretical statistics. However, technical details are delayed until the last chapter such that mathematically able readers without knowledge of the rigorous theory of probability will have no trouble understanding most of the book.

The Jackknife and Bootstrap


Author: Jun Shao,Dongsheng Tu
Publisher: Springer Science & Business Media
ISBN: 1461207959
Category: Mathematics
Page: 517
View: 5156

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The jackknife and bootstrap are the most popular data-resampling meth ods used in statistical analysis. The resampling methods replace theoreti cal derivations required in applying traditional methods (such as substitu tion and linearization) in statistical analysis by repeatedly resampling the original data and making inferences from the resamples. Because of the availability of inexpensive and fast computing, these computer-intensive methods have caught on very rapidly in recent years and are particularly appreciated by applied statisticians. The primary aims of this book are (1) to provide a systematic introduction to the theory of the jackknife, the bootstrap, and other resampling methods developed in the last twenty years; (2) to provide a guide for applied statisticians: practitioners often use (or misuse) the resampling methods in situations where no theoretical confirmation has been made; and (3) to stimulate the use of the jackknife and bootstrap and further devel opments of the resampling methods. The theoretical properties of the jackknife and bootstrap methods are studied in this book in an asymptotic framework. Theorems are illustrated by examples. Finite sample properties of the jackknife and bootstrap are mostly investigated by examples and/or empirical simulation studies. In addition to the theory for the jackknife and bootstrap methods in problems with independent and identically distributed (Li.d.) data, we try to cover, as much as we can, the applications of the jackknife and bootstrap in various complicated non-Li.d. data problems.

Resampling Methods for Dependent Data


Author: S. N. Lahiri
Publisher: Springer Science & Business Media
ISBN: 147573803X
Category: Mathematics
Page: 374
View: 9616

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By giving a detailed account of bootstrap methods and their properties for dependent data, this book provides illustrative numerical examples throughout. The book fills a gap in the literature covering research on re-sampling methods for dependent data that has witnessed vigorous growth over the last two decades but remains scattered in various statistics and econometrics journals. It can be used as a graduate level text and also as a research monograph for statisticians and econometricians.

Permutation Tests

A Practical Guide to Resampling Methods for Testing Hypotheses
Author: Phillip Good
Publisher: Springer Science & Business Media
ISBN: 147573235X
Category: Mathematics
Page: 271
View: 5917

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A step-by-step manual on the application of permutation tests in biology, business, medicine, science, and engineering. Its intuitive and informal style make it ideal for students and researchers, whether experienced or coming to these resampling methods for the first time. The real-world problems of missing and censored data, multiple comparisons, nonresponders, after-the-fact covariates, and outliers are all dealt with at length. This new edition has more than 100 additional pages, and includes streamlined statistics for the k-sample comparison and analysis of variance plus expanded sections on computational techniques, multiple comparisons, multiple regression, comparing variances, and testing interactions in balanced designs. The comprehensive author and subject indexes, plus an expert-system guide to methods, provide for further ease of use, while the exercises at the end of every chapter have been supplemented with drills and a number of graduate-level thesis problems.

Asymptotic Theory of Statistics and Probability


Author: Anirban DasGupta
Publisher: Springer Science & Business Media
ISBN: 0387759700
Category: Mathematics
Page: 722
View: 9191

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This unique book delivers an encyclopedic treatment of classic as well as contemporary large sample theory, dealing with both statistical problems and probabilistic issues and tools. The book is unique in its detailed coverage of fundamental topics. 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. There is no other book in large sample theory that matches this book in coverage, exercises and examples, bibliography, and lucid conceptual discussion of issues and theorems.

Bootstrap Methods and Their Application


Author: A. C. Davison,D. V. Hinkley
Publisher: Cambridge University Press
ISBN: 9780521574716
Category: Computers
Page: 582
View: 6859

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This book gives a broad and up-to-date coverage of bootstrap methods, with numerous applied examples, developed in a coherent way with the necessary theoretical basis. Applications include stratified data; finite populations; censored and missing data; linear, nonlinear, and smooth regression models; classification; time series and spatial problems. Special features of the book include: extensive discussion of significance tests and confidence intervals; material on various diagnostic methods; and methods for efficient computation, including improved Monte Carlo simulation. Each chapter includes both practical and theoretical exercises. Included with the book is a disk of purpose-written S-Plus programs for implementing the methods described in the text. Computer algorithms are clearly described, and computer code is included on a 3-inch, 1.4M disk for use with IBM computers and compatible machines. Users must have the S-Plus computer application. Author resource page: http://statwww.epfl.ch/davison/BMA/

An Introduction to the Bootstrap


Author: Bradley Efron,R.J. Tibshirani
Publisher: CRC Press
ISBN: 9780412042317
Category: Mathematics
Page: 456
View: 677

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Statistics is a subject of many uses and surprisingly few effective practitioners. The traditional road to statistical knowledge is blocked, for most, by a formidable wall of mathematics. The approach in An Introduction to the Bootstrap avoids that wall. It arms scientists and engineers, as well as statisticians, with the computational techniques they need to analyze and understand complicated data sets.

Counterexamples in Probability And Statistics


Author: A.F. Siegel
Publisher: Routledge
ISBN: 1351457632
Category: Mathematics
Page: 328
View: 6879

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This volume contains six early mathematical works, four papers on fiducial inference, five on transformations, and twenty-seven on a miscellany of topics in mathematical statistics. Several previously unpublished works are included.

Handbook of Statistics

Time Series Analysis: Methods and Applications
Author: N.A
Publisher: Elsevier
ISBN: 0444538631
Category: Mathematics
Page: 776
View: 9395

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The field of statistics not only affects all areas of scientific activity, but also many other matters such as public policy. It is branching rapidly into so many different subjects that a series of handbooks is the only way of comprehensively presenting the various aspects of statistical methodology, applications, and recent developments. The Handbook of Statistics is a series of self-contained reference books. Each volume is devoted to a particular topic in statistics, with Volume 30 dealing with time series. The series is addressed to the entire community of statisticians and scientists in various disciplines who use statistical methodology in their work. At the same time, special emphasis is placed on applications-oriented techniques, with the applied statistician in mind as the primary audience. Comprehensively presents the various aspects of statistical methodology Discusses a wide variety of diverse applications and recent developments Contributors are internationally renowened experts in their respective areas

Time Series Analysis

Methods and Applications
Author: Tata Subba Rao,Suhasini Subba Rao,Calyampudi Radhakrishna Rao
Publisher: Elsevier
ISBN: 0444538585
Category: Mathematics
Page: 755
View: 1164

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The field of statistics not only affects all areas of scientific activity, but also many other matters such as public policy. It is branching rapidly into so many different subjects that a series of handbooks is the only way of comprehensively presenting the various aspects of statistical methodology, applications, and recent developments. The Handbook of Statistics is a series of self-contained reference books. Each volume is devoted to a particular topic in statistics, with Volume 30 dealing with time series. The series is addressed to the entire community of statisticians and scientists in various disciplines who use statistical methodology in their work. At the same time, special emphasis is placed on applications-oriented techniques, with the applied statistician in mind as the primary audience. Comprehensively presents the various aspects of statistical methodology Discusses a wide variety of diverse applications and recent developments Contributors are internationally renowened experts in their respective areas

When Does Bootstrap Work?

Asymptotic Results and Simulations
Author: Enno Mammen
Publisher: Springer Science & Business Media
ISBN: 1461229502
Category: Mathematics
Page: 201
View: 1501

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Martingale Limit Theory and Its Application


Author: P. Hall,C. C. Heyde
Publisher: Academic Press
ISBN: 1483263223
Category: Mathematics
Page: 320
View: 3942

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Martingale Limit Theory and Its Application discusses the asymptotic properties of martingales, particularly as regards key prototype of probabilistic behavior that has wide applications. The book explains the thesis that martingale theory is central to probability theory, and also examines the relationships between martingales and processes embeddable in or approximated by Brownian motion. The text reviews the martingale convergence theorem, the classical limit theory and analogs, and the martingale limit theorems viewed as the rate of convergence results in the martingale convergence theorem. The book explains the square function inequalities, weak law of large numbers, as well as the strong law of large numbers. The text discusses the reverse martingales, martingale tail sums, the invariance principles in the central limit theorem, and also the law of the iterated logarithm. The book investigates the limit theory for stationary processes via corresponding results for approximating martingales and the estimation of parameters from stochastic processes. The text can be profitably used as a reference for mathematicians, advanced students, and professors of higher mathematics or statistics.

Theory of Nonparametric Tests


Author: Thorsten Dickhaus
Publisher: Springer
ISBN: 3319763156
Category: Mathematics
Page: 124
View: 6184

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This textbook provides a self-contained presentation of the main concepts and methods of nonparametric statistical testing, with a particular focus on the theoretical foundations of goodness-of-fit tests, rank tests, resampling tests, and projection tests. The substitution principle is employed as a unified approach to the nonparametric test problems discussed. In addition to mathematical theory, it also includes numerous examples and computer implementations. The book is intended for advanced undergraduate, graduate, and postdoc students as well as young researchers. Readers should be familiar with the basic concepts of mathematical statistics typically covered in introductory statistics courses.

All of Nonparametric Statistics


Author: Larry Wasserman
Publisher: Springer Science & Business Media
ISBN: 9780387306230
Category: Mathematics
Page: 270
View: 1202

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This text provides the reader with a single book where they can find accounts of a number of up-to-date issues in nonparametric inference. The book is aimed at Masters or PhD level students in statistics, computer science, and engineering. It is also suitable for researchers who want to get up to speed quickly on modern nonparametric methods. It covers a wide range of topics including the bootstrap, the nonparametric delta method, nonparametric regression, density estimation, orthogonal function methods, minimax estimation, nonparametric confidence sets, and wavelets. The book’s dual approach includes a mixture of methodology and theory.

A Course in Mathematical Statistics and Large Sample Theory


Author: Rabi Bhattacharya,Lizhen Lin,Victor Patrangenaru
Publisher: Springer
ISBN: 1493940325
Category: Mathematics
Page: 389
View: 3923

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This graduate-level textbook is primarily aimed at graduate students of statistics, mathematics, science, and engineering who have had an undergraduate course in statistics, an upper division course in analysis, and some acquaintance with measure theoretic probability. It provides a rigorous presentation of the core of mathematical statistics. Part I of this book constitutes a one-semester course on basic parametric mathematical statistics. Part II deals with the large sample theory of statistics - parametric and nonparametric, and its contents may be covered in one semester as well. Part III provides brief accounts of a number of topics of current interest for practitioners and other disciplines whose work involves statistical methods.

Empirical Likelihood


Author: Art B. Owen
Publisher: CRC Press
ISBN: 1420036157
Category: Mathematics
Page: 304
View: 1402

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Empirical likelihood provides inferences whose validity does not depend on specifying a parametric model for the data. Because it uses a likelihood, the method has certain inherent advantages over resampling methods: it uses the data to determine the shape of the confidence regions, and it makes it easy to combined data from multiple sources. It also facilitates incorporating side information, and it simplifies accounting for censored, truncated, or biased sampling. One of the first books published on the subject, Empirical Likelihood offers an in-depth treatment of this method for constructing confidence regions and testing hypotheses. The author applies empirical likelihood to a range of problems, from those as simple as setting a confidence region for a univariate mean under IID sampling, to problems defined through smooth functions of means, regression models, generalized linear models, estimating equations, or kernel smooths, and to sampling with non-identically distributed data. Abundant figures offer visual reinforcement of the concepts and techniques. Examples from a variety of disciplines and detailed descriptions of algorithms-also posted on a companion Web site at-illustrate the methods in practice. Exercises help readers to understand and apply the methods. The method of empirical likelihood is now attracting serious attention from researchers in econometrics and biostatistics, as well as from statisticians. This book is your opportunity to explore its foundations, its advantages, and its application to a myriad of practical problems.

Numerical Analysis for Statisticians


Author: Kenneth Lange
Publisher: Springer Science & Business Media
ISBN: 1441959459
Category: Business & Economics
Page: 600
View: 359

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Numerical analysis is the study of computation and its accuracy, stability and often its implementation on a computer. This book focuses on the principles of numerical analysis and is intended to equip those readers who use statistics to craft their own software and to understand the advantages and disadvantages of different numerical methods.

Breakthroughs in Statistics

Foundations and basic theory. Volume I
Author: Samuel Kotz,Norman L. Johnson
Publisher: Springer Science & Business Media
ISBN: 9780387940373
Category: Mathematics
Page: 632
View: 2335

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McCrimmon, having gotten Grierson's attention, continued: "A breakthrough, you say? If it's in economics, at least it can't be dangerous. Nothing like gene engineering, laser beams, sex hormones or international relations. That's where we don't want any breakthroughs. " (Galbraith, 1. K. (1990) A Tenured Profes­ sor, Houghton Miffiin; Boston. ) To judge [astronomy] in this way [a narrow utilitarian point of view] demon­ strates not only how poor we are, but also how small, narrow, and indolent our minds are; it shows a disposition always to calculate the payolIbefore the work, a cold heart and a lack of feeling for everything that is great and honors man. One can unfortunately not deny that such a mode of thinking is not uncommon in our age, and I am convinced that this is closely connected with the catastro­ phes which have befallen many countries in recent times; do not mistake me, I do not talk of the general lack of concern for science, but of the source from which all this has come, of the tendency to everywhere look out for one's advan­ tage and to relate everything to one's physical well-being, of the indilIerence towards great ideas, ofthe aversion to any elIort which derives from pure enthu­ siasm: I believe that such attitudes, if they prevail, can be decisive in catas­ trophes of the kind we have experienced. [Gauss, K. F. : Astronomische An­ trittsvorlesung (cited from Buhler, W. K. (1981) Gauss: A Biographical Study, Springer: New York)].

Nonparametric Econometrics

Theory and Practice
Author: Qi Li,Jeffrey Scott Racine
Publisher: Princeton University Press
ISBN: 1400841062
Category: Business & Economics
Page: 768
View: 8265

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Until now, students and researchers in nonparametric and semiparametric statistics and econometrics have had to turn to the latest journal articles to keep pace with these emerging methods of economic analysis. Nonparametric Econometrics fills a major gap by gathering together the most up-to-date theory and techniques and presenting them in a remarkably straightforward and accessible format. The empirical tests, data, and exercises included in this textbook help make it the ideal introduction for graduate students and an indispensable resource for researchers. Nonparametric and semiparametric methods have attracted a great deal of attention from statisticians in recent decades. While the majority of existing books on the subject operate from the presumption that the underlying data is strictly continuous in nature, more often than not social scientists deal with categorical data--nominal and ordinal--in applied settings. The conventional nonparametric approach to dealing with the presence of discrete variables is acknowledged to be unsatisfactory. This book is tailored to the needs of applied econometricians and social scientists. Qi Li and Jeffrey Racine emphasize nonparametric techniques suited to the rich array of data types--continuous, nominal, and ordinal--within one coherent framework. They also emphasize the properties of nonparametric estimators in the presence of potentially irrelevant variables. Nonparametric Econometrics covers all the material necessary to understand and apply nonparametric methods for real-world problems.

Trends and Perspectives in Linear Statistical Inference

LinStat, Istanbul, August 2016
Author: Müjgan Tez,Dietrich von Rosen
Publisher: Springer
ISBN: 3319732412
Category: Mathematics
Page: 257
View: 3494

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This volume features selected contributions on a variety of topics related to linear statistical inference. The peer-reviewed papers from the International Conference on Trends and Perspectives in Linear Statistical Inference (LinStat 2016) held in Istanbul, Turkey, 22-25 August 2016, cover topics in both theoretical and applied statistics, such as linear models, high-dimensional statistics, computational statistics, the design of experiments, and multivariate analysis. The book is intended for statisticians, Ph.D. students, and professionals who are interested in statistical inference.