The Bootstrap and Edgeworth Expansion


Author: Peter Hall
Publisher: Springer Science & Business Media
ISBN: 146124384X
Category: Mathematics
Page: 354
View: 9338

Continue Reading →

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: 1334

Continue Reading →

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.

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: 3601

Continue Reading →

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: 2369

Continue Reading →

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.

Resampling Methods for Dependent Data


Author: S. N. Lahiri
Publisher: Springer Science & Business Media
ISBN: 147573803X
Category: Mathematics
Page: 374
View: 2620

Continue Reading →

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.

An Introduction to the Bootstrap


Author: Bradley Efron,R.J. Tibshirani
Publisher: CRC Press
ISBN: 9780412042317
Category: Mathematics
Page: 456
View: 7615

Continue Reading →

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.

Martingale Limit Theory and Its Application


Author: P. Hall,C. C. Heyde
Publisher: Academic Press
ISBN: 1483263223
Category: Mathematics
Page: 320
View: 9268

Continue Reading →

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.

All of Nonparametric Statistics


Author: Larry Wasserman
Publisher: Springer Science & Business Media
ISBN: 9780387306230
Category: Mathematics
Page: 270
View: 1350

Continue Reading →

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.

Asymptotic Theory of Statistical Inference for Time Series


Author: Masanobu Taniguchi,Yoshihide Kakizawa
Publisher: Springer Science & Business Media
ISBN: 146121162X
Category: Mathematics
Page: 662
View: 3474

Continue Reading →

The primary aim of this book is to provide modern statistical techniques and theory for stochastic processes. The stochastic processes mentioned here are not restricted to the usual AR, MA, and ARMA processes. A wide variety of stochastic processes, including non-Gaussian linear processes, long-memory processes, nonlinear processes, non-ergodic processes and diffusion processes are described. The authors discuss estimation and testing theory and many other relevant statistical methods and techniques.

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: 5850

Continue Reading →

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.

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: 2308

Continue Reading →

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)].

Bayesian Forecasting and Dynamic Models


Author: Mike West,Jeff Harrison
Publisher: Springer Science & Business Media
ISBN: 1475793650
Category: Mathematics
Page: 704
View: 4484

Continue Reading →

In this book we are concerned with Bayesian learning and forecast ing in dynamic environments. We describe the structure and theory of classes of dynamic models, and their uses in Bayesian forecasting. The principles, models and methods of Bayesian forecasting have been developed extensively during the last twenty years. This devel opment has involved thorough investigation of mathematical and sta tistical aspects of forecasting models and related techniques. With this has come experience with application in a variety of areas in commercial and industrial, scientific and socio-economic fields. In deed much of the technical development has been driven by the needs of forecasting practitioners. As a result, there now exists a relatively complete statistical and mathematical framework, although much of this is either not properly documented or not easily accessible. Our primary goals in writing this book have been to present our view of this approach to modelling and forecasting, and to provide a rea sonably complete text for advanced university students and research workers. The text is primarily intended for advanced undergraduate and postgraduate students in statistics and mathematics. In line with this objective we present thorough discussion of mathematical and statistical features of Bayesian analyses of dynamic models, with illustrations, examples and exercises in each Chapter.

Introduction to Reliability Analysis

Probability Models and Statistical Methods
Author: Shelemyahu Zacks
Publisher: Springer Science & Business Media
ISBN: 1461228549
Category: Mathematics
Page: 212
View: 1091

Continue Reading →

Reliability analysis is concerned with the analysis of devices and systems whose individual components are prone to failure. This textbook presents an introduction to reliability analysis of repairable and non-repairable systems. It is based on courses given to both undergraduate and graduate students of engineering and statistics as well as in workshops for professional engineers and scientists. As aresult, the book concentrates on the methodology of the subject and on understanding theoretical results rather than on its theoretical development. An intrinsic aspect of reliability analysis is that the failure of components is best modelled using techniques drawn from probability and statistics. Professor Zacks covers all the basic concepts required from these subjects and covers the main modern reliability analysis techniques thoroughly. These include: the graphical analysis of life data, maximum likelihood estimation and bayesian likelihood estimation. Throughout the emphasis is on the practicalities of the subject with numerous examples drawn from industrial and engineering settings.

Handbook of Statistics

Time Series Analysis: Methods and Applications
Author: N.A
Publisher: Elsevier
ISBN: 0444538631
Category: Mathematics
Page: 776
View: 4683

Continue Reading →

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

Aspects of Risk Theory


Author: Jan Grandell
Publisher: Springer Science & Business Media
ISBN: 1461390583
Category: Mathematics
Page: 175
View: 7138

Continue Reading →

Risk theory, which deals with stochastic models of an insurance business, is a classical application of probability theory. The fundamental problem in risk theory is to investigate the ruin possibility of the risk business. Traditionally the occurrence of the claims is described by a Poisson process and the cost of the claims by a sequence of random variables. This book is a treatise of risk theory with emphasis on models where the occurrence of the claims is described by more general point processes than the Poisson process, such as renewal processes, Cox processes and general stationary point processes. In the Cox case the possibility of risk fluctuation is explicitly taken into account. The presentation is based on modern probabilistic methods rather than on analytic methods. The theory is accompanied with discussions on practical evaluation of ruin probabilities and statistical estimation. Many numerical illustrations of the results are given.

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: 9348

Continue Reading →

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

Numerical Analysis for Statisticians


Author: Kenneth Lange
Publisher: Springer Science & Business Media
ISBN: 1441959459
Category: Business & Economics
Page: 600
View: 6179

Continue Reading →

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.

Theory of Nonparametric Tests


Author: Thorsten Dickhaus
Publisher: Springer
ISBN: 3319763156
Category: Mathematics
Page: 124
View: 4336

Continue Reading →

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.

Correlation Theory of Stationary and Related Random Functions

Supplementary Notes and References
Author: A.M. Yaglom
Publisher: Springer Science & Business Media
ISBN: 1461246288
Category: Mathematics
Page: 258
View: 4048

Continue Reading →

Correlation Theory of Stationary and Related Random Functions is an elementary introduction to the most important part of the theory dealing only with the first and second moments of these functions. This theory is a significant part of modern probability theory and offers both intrinsic mathematical interest and many concrete and practical applications. Stationary random functions arise in connection with stationary time series which are so important in many areas of engineering and other applications. This book presents the theory in such a way that it can be understood by readers without specialized mathematical backgrounds, requiring only the knowledge of elementary calculus. The first volume in this two-volume exposition contains the main theory; the supplementary notes and references of the second volume consist of detailed discussions of more specialized questions, some more additional material (which assumes a more thorough mathematical background than the rest of the book) and numerous references to the extensive literature.

Bootstrap Methods

A Guide for Practitioners and Researchers
Author: Michael R. Chernick
Publisher: John Wiley & Sons
ISBN: 1118211596
Category: Mathematics
Page: 400
View: 2381

Continue Reading →

A practical and accessible introduction to the bootstrap method——newly revised and updated Over the past decade, the application of bootstrap methods to new areas of study has expanded, resulting in theoretical and applied advances across various fields. Bootstrap Methods, Second Edition is a highly approachable guide to the multidisciplinary, real-world uses of bootstrapping and is ideal for readers who have a professional interest in its methods, but are without an advanced background in mathematics. Updated to reflect current techniques and the most up-to-date work on the topic, the Second Edition features: The addition of a second, extended bibliography devoted solely to publications from 1999–2007, which is a valuable collection of references on the latest research in the field A discussion of the new areas of applicability for bootstrap methods, including use in the pharmaceutical industry for estimating individual and population bioequivalence in clinical trials A revised chapter on when and why bootstrap fails and remedies for overcoming these drawbacks Added coverage on regression, censored data applications, P-value adjustment, ratio estimators, and missing data New examples and illustrations as well as extensive historical notes at the end of each chapter With a strong focus on application, detailed explanations of methodology, and complete coverage of modern developments in the field, Bootstrap Methods, Second Edition is an indispensable reference for applied statisticians, engineers, scientists, clinicians, and other practitioners who regularly use statistical methods in research. It is also suitable as a supplementary text for courses in statistics and resampling methods at the upper-undergraduate and graduate levels.