Asymptotic Theory For Bootstrap Methods In Statistics
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Asymptotic Theory For Bootstrap Methods In Statistics
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Author : Rudolf J. Beran
language : en
Publisher: Publications CRM
Release Date : 1991
Asymptotic Theory For Bootstrap Methods In Statistics written by Rudolf J. Beran and has been published by Publications CRM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Asymptotic efficiencies (Statistics) categories.
Degenerate U And V Statistics Under Weak Dependence
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Author : Anne Leucht
language : en
Publisher:
Release Date : 2011
Degenerate U And V Statistics Under Weak Dependence written by Anne Leucht and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.
Numerous test statistics can be approximated by statistics of U- or V-type. In the case of i.i.d. random variables the limit distribution can be derived by a spectral decomposition of the kernel if the latter is square integrable. To use the same method for dependent data, restrictive assumptions on the associated eigenvalues and eigenfunctions are required. In the majority of cases, it is quite complicated or even impossible to check these conditions. Therefore we employ a wavelet decomposition of the kernel in order to derive the asymptotic distributions of U- and V-statistics for weakly dependent data. This approach only requires some moment constraints and smoothness assumptions concerning the kernel. The asymptotic distributions of U- and V-statistics for both independent and weakly dependent observations cannot be used directly since they depend on certain parameters, which in turn depend on the underlying situation in a complicated way. Therefore, problems arise as soon as critical values for test statistics of U- and V-type have to be determined. The bootstrap offers a convenient way to circumvent these problems, see [3] for the i.i.d. case. We derive the consistency of general bootstrap methods for statistics of weakly dependent data.
Bootstrap Methods
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Author : Gerhard Dikta
language : en
Publisher: Springer Nature
Release Date : 2021-08-10
Bootstrap Methods written by Gerhard Dikta and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-10 with Mathematics categories.
This book provides a compact introduction to the bootstrap method. In addition to classical results on point estimation and test theory, multivariate linear regression models and generalized linear models are covered in detail. Special attention is given to the use of bootstrap procedures to perform goodness-of-fit tests to validate model or distributional assumptions. In some cases, new methods are presented here for the first time. The text is motivated by practical examples and the implementations of the corresponding algorithms are always given directly in R in a comprehensible form. Overall, R is given great importance throughout. Each chapter includes a section of exercises and, for the more mathematically inclined readers, concludes with rigorous proofs. The intended audience is graduate students who already have a prior knowledge of probability theory and mathematical statistics.
Bootstrap Methods
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Author : Michael R. Chernick
language : en
Publisher: John Wiley & Sons
Release Date : 2011-09-23
Bootstrap Methods written by Michael R. Chernick 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 2011-09-23 with Mathematics categories.
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.
Non Standard Parametric Statistical Inference
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Author : Russell Cheng
language : en
Publisher: Oxford University Press
Release Date : 2017
Non Standard Parametric Statistical Inference written by Russell Cheng and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Mathematics categories.
This book discusses the fitting of parametric statistical models to data samples. Emphasis is placed on: (i) how to recognize situations where the problem is non-standard when parameter estimates behave unusually, and (ii) the use of parametric bootstrap resampling methods in analyzing such problems. A frequentist likelihood-based viewpoint is adopted, for which there is a well-established and very practical theory. The standard situation is where certain widely applicable regularity conditions hold. However, there are many apparently innocuous situations where standard theory breaks down, sometimes spectacularly. Most of the departures from regularity are described geometrically, with only sufficient mathematical detail to clarify the non-standard nature of a problem and to allow formulation of practical solutions. The book is intended for anyone with a basic knowledge of statistical methods, as is typically covered in a university statistical inference course, wishing to understand or study how standard methodology might fail. Easy to understand statistical methods are presented which overcome these difficulties, and demonstrated by detailed examples drawn from real applications. Simple and practical model-building is an underlying theme. Parametric bootstrap resampling is used throughout for analyzing the properties of fitted models, illustrating its ease of implementation even in non-standard situations. Distributional properties are obtained numerically for estimators or statistics not previously considered in the literature because their theoretical distributional properties are too hard to obtain theoretically. Bootstrap results are presented mainly graphically in the book, providing an accessible demonstration of the sampling behaviour of estimators.
Bootstrap Tests For Regression Models
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Author : L. Godfrey
language : en
Publisher: Springer
Release Date : 2009-07-29
Bootstrap Tests For Regression Models written by L. Godfrey and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-29 with Business & Economics categories.
An accessible discussion examining computationally-intensive techniques and bootstrap methods, providing ways to improve the finite-sample performance of well-known asymptotic tests for regression models. This book uses the linear regression model as a framework for introducing simulation-based tests to help perform econometric analyses.
An Introduction To Bootstrap Methods With Applications To R
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Author : Michael R. Chernick
language : en
Publisher: John Wiley & Sons
Release Date : 2014-08-21
An Introduction To Bootstrap Methods With Applications To R written by Michael R. Chernick 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 2014-08-21 with Mathematics categories.
A comprehensive introduction to bootstrap methods in the Rprogramming environment Bootstrap methods provide a powerful approach to statisticaldata analysis, as they have more general applications than standardparametric methods. An Introduction to Bootstrap Methods withApplications to R explores the practicality of this approach andsuccessfully utilizes R to illustrate applications for thebootstrap and other resampling methods. This book provides a modernintroduction to bootstrap methods for readers who do not have anextensive background in advanced mathematics. Emphasis throughoutis on the use of bootstrap methods as an exploratory tool,including its value in variable selection and other modelingenvironments. The authors begin with a description of bootstrap methods andits relationship to other resampling methods, along with anoverview of the wide variety of applications of the approach.Subsequent chapters offer coverage of improved confidence setestimation, estimation of error rates in discriminant analysis, andapplications to a wide variety of hypothesis testing and estimationproblems, including pharmaceutical, genomics, and economics. Toinform readers on the limitations of the method, the book alsoexhibits counterexamples to the consistency of bootstrapmethods. An introduction to R programming provides the needed preparationto work with the numerous exercises and applications presentedthroughout the book. A related website houses the book's Rsubroutines, and an extensive listing of references providesresources for further study. Discussing the topic at a remarkably practical and accessiblelevel, An Introduction to Bootstrap Methods with Applications to Ris an excellent book for introductory courses on bootstrap andresampling methods at the upper-undergraduate and graduate levels.It also serves as an insightful reference for practitioners workingwith data in engineering, medicine, and the social sciences whowould like to acquire a basic understanding of bootstrapmethods.
The Jackknife And Bootstrap
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Author : Jun Shao
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Jackknife And Bootstrap written by Jun Shao 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 2012-12-06 with Mathematics categories.
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.
Asymptotic Theory Of Statistics And Probability
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Author : Anirban DasGupta
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-02-06
Asymptotic Theory Of Statistics And Probability written by Anirban DasGupta 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 2008-02-06 with Mathematics categories.
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.
An Introduction To The Bootstrap
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Author : Bradley Efron
language : en
Publisher: CRC Press
Release Date : 1994-05-15
An Introduction To The Bootstrap written by Bradley Efron and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-05-15 with Mathematics categories.
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.