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Author: Viktor Subbotin Publisher: ISBN: Category : Languages : en Pages : 61
Book Description
The paper develops the bootstrap theory and extends the asymptotic theory of rank estimators, such as the Maximum Rank Correlation Estimator (MRC) of Han (1987), Monotone Rank Estimator (MR) of Cavanagh and Sherman (1998) or Pairwise-Difference Rank Estimators (PDR) of Abrevaya (2003). It is known that under general conditions these estimators have asymptotic normal distributions, but the asymptotic variances are difficult to find. Here we prove that the quantiles and the variances of the asymptotic distributions can be consistently estimated by the nonparametric bootstrap. We investigate the accuracy of inference based on the asymptotic approximation and the bootstrap, and provide bounds on the associated error. In the case of MRC and MR, the bound is a function of the sample size of order close to n^(-1/6). The PDR estimators belong to a special subclass of rank estimators for which the bound is vanishing with the rate close to n^(-1/2). The theoretical findings are illustrated with Monte-Carlo experiments and a real data example.
Author: Viktor Subbotin Publisher: ISBN: Category : Languages : en Pages : 61
Book Description
The paper develops the bootstrap theory and extends the asymptotic theory of rank estimators, such as the Maximum Rank Correlation Estimator (MRC) of Han (1987), Monotone Rank Estimator (MR) of Cavanagh and Sherman (1998) or Pairwise-Difference Rank Estimators (PDR) of Abrevaya (2003). It is known that under general conditions these estimators have asymptotic normal distributions, but the asymptotic variances are difficult to find. Here we prove that the quantiles and the variances of the asymptotic distributions can be consistently estimated by the nonparametric bootstrap. We investigate the accuracy of inference based on the asymptotic approximation and the bootstrap, and provide bounds on the associated error. In the case of MRC and MR, the bound is a function of the sample size of order close to n^(-1/6). The PDR estimators belong to a special subclass of rank estimators for which the bound is vanishing with the rate close to n^(-1/2). The theoretical findings are illustrated with Monte-Carlo experiments and a real data example.
Author: Jonas Böhmer Publisher: GRIN Verlag ISBN: 3640421833 Category : Mathematics Languages : en Pages : 61
Book Description
Diploma Thesis from the year 2009 in the subject Statistics, grade: 1,6, University of Bonn (Statistische Abteilung der Rechts- und Staatswissenschaftlichen Fakult t), course: Diplomarbeit bei Prof.Dr. Alois Kneip, language: English, abstract: The statistical technique called bootstrap is usable with a lot of inferential problems and it is the main topic of this paper. Since the bootstrap provides material for a whole series of books it is essential to pick one special aspect of the bootstrap and investigate it in depth, otherwise the analysis would inevitably become too general. This aspect is the topic of regression. Hence, this paper will introduce the bootstrap and compare the performance of the new inference methods which it provides with some classical methods of judging a regression which were used in the years before the bootstrap. Therefore the remainder of this paper is as follows: First there will be a description of the basic model in which all of the following investigations will be done, chapter two. The next chapter will describe the different regression techniques which try to solve the model. The fourth chapter is going to show the behavior of these regression techniques in large samples, i.e. shows some classical methods of statistical inference. Following chapter five will give an introduction to the bootstrap which will be succeeded by a description of the bootstrap in regression problems, chapter six. The seventh chapter will show how inference is done with the help of the bootstrap. The eighth chapter is going to compare the performances of classical and bootstrap inference in regressions. Before the concluding remarks of chapter ten, there will be a practical application in chapter nine which tries to prove some observations of the preceeding chapters.
Author: Jonas Böhmer Publisher: GRIN Verlag ISBN: 3640422414 Category : Mathematics Languages : en Pages : 54
Book Description
Diploma Thesis from the year 2009 in the subject Mathematics - Statistics, grade: 1,6, University of Bonn (Statistische Abteilung der Rechts- und Staatswissenschaftlichen Fakultät), course: Diplomarbeit bei Prof.Dr. Alois Kneip, language: English, abstract: The statistical technique called bootstrap is usable with a lot of inferential problems and it is the main topic of this paper. Since the bootstrap provides material for a whole series of books it is essential to pick one special aspect of the bootstrap and investigate it in depth, otherwise the analysis would inevitably become too general. This aspect is the topic of regression. Hence, this paper will introduce the bootstrap and compare the performance of the new inference methods which it provides with some classical methods of judging a regression which were used in the years before the bootstrap. Therefore the remainder of this paper is as follows: First there will be a description of the basic model in which all of the following investigations will be done, chapter two. The next chapter will describe the different regression techniques which try to solve the model. The fourth chapter is going to show the behavior of these regression techniques in large samples, i.e. shows some classical methods of statistical inference. Following chapter five will give an introduction to the bootstrap which will be succeeded by a description of the bootstrap in regression problems, chapter six. The seventh chapter will show how inference is done with the help of the bootstrap. The eighth chapter is going to compare the performances of classical and bootstrap inference in regressions. Before the concluding remarks of chapter ten, there will be a practical application in chapter nine which tries to prove some observations of the preceeding chapters.
Author: Michael R. Chernick Publisher: John Wiley & Sons ISBN: 1118211596 Category : Mathematics Languages : en Pages : 337
Book Description
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.
Author: Connie Page Publisher: Springer Science & Business Media ISBN: 1461228565 Category : Mathematics Languages : en Pages : 595
Book Description
Interface '90 is the continuation of an ext!remely successful symposium series. The series has provided a forum for the interaction of professionals in statistics, computing science, and in numerical methods, wherein they may discuss a wide range of topics at the interface of these disciplines. This, the 22nd Symposium on the Interface: Computing Science and Statistics, was held 16-19 May, 1990 at the Kellogg Center on the campus of Michigan State University and is the third Symposium to be held under the recently organized Interface Foundation of North America. The Interface Board of Directors consists of the nine most recent Symposium Chairs: James E. Gentle, Lynne Billard, David M. Allen, Thomas J. Boardman, Richard M. Heiberger, Edward J. Wegman, Linda Malone, Raoul LePage, and Jon Kettenring. The officers of the Interface are William Eddy, Board Chairman and Executive Director; Edward Wegman, President and Treasurer; Lynne Billard, Secretary. My valued colleague Connie Page, Editor of this Proceedings Volume and generally bright and hardworking person, has organizational skills of a higher order which were successfully brought into play during many critical junctures not strictly connected with the Proceedings. Edward Wegman, Barbara Barringer, Bill Eddy, and George Styan all pitched in with useful information on numerous occasions. Our Keynote Speaker, Peter G. Hall and Plenary Speakers David L. Donoho, Jerome H. Friedman (who also gave a short course), Bruce Hajek, John Skilling, and C. F.
Author: Roger Koenker Publisher: CRC Press ISBN: 1498725295 Category : Mathematics Languages : en Pages : 463
Book Description
Quantile regression constitutes an ensemble of statistical techniques intended to estimate and draw inferences about conditional quantile functions. Median regression, as introduced in the 18th century by Boscovich and Laplace, is a special case. In contrast to conventional mean regression that minimizes sums of squared residuals, median regression minimizes sums of absolute residuals; quantile regression simply replaces symmetric absolute loss by asymmetric linear loss. Since its introduction in the 1970's by Koenker and Bassett, quantile regression has been gradually extended to a wide variety of data analytic settings including time series, survival analysis, and longitudinal data. By focusing attention on local slices of the conditional distribution of response variables it is capable of providing a more complete, more nuanced view of heterogeneous covariate effects. Applications of quantile regression can now be found throughout the sciences, including astrophysics, chemistry, ecology, economics, finance, genomics, medicine, and meteorology. Software for quantile regression is now widely available in all the major statistical computing environments. The objective of this volume is to provide a comprehensive review of recent developments of quantile regression methodology illustrating its applicability in a wide range of scientific settings. The intended audience of the volume is researchers and graduate students across a diverse set of disciplines.
Author: David R. Hunter Publisher: World Scientific ISBN: 9814340561 Category : Electronic books Languages : en Pages : 370
Book Description
This festschrift includes papers authored by many collaborators, colleagues, and students of Professor Thomas P Hettmansperger, who worked in research in nonparametric statistics, rank statistics, robustness, and mixture models during a career that spanned nearly 40 years. It is a broad sample of peer-reviewed, cutting-edge research related to nonparametrics and mixture models.
Author: Per K. Andersen Publisher: Springer Science & Business Media ISBN: 1461243483 Category : Mathematics Languages : en Pages : 779
Book Description
Modern survival analysis and more general event history analysis may be effectively handled within the mathematical framework of counting processes. This book presents this theory, which has been the subject of intense research activity over the past 15 years. The exposition of the theory is integrated with careful presentation of many practical examples, drawn almost exclusively from the authors'own experience, with detailed numerical and graphical illustrations. Although Statistical Models Based on Counting Processes may be viewed as a research monograph for mathematical statisticians and biostatisticians, almost all the methods are given in concrete detail for use in practice by other mathematically oriented researchers studying event histories (demographers, econometricians, epidemiologists, actuarial mathematicians, reliability engineers and biologists). Much of the material has so far only been available in the journal literature (if at all), and so a wide variety of researchers will find this an invaluable survey of the subject.
Author: Bruce Hansen Publisher: Princeton University Press ISBN: 0691235899 Category : Business & Economics Languages : en Pages : 1080
Book Description
The most authoritative and up-to-date core econometrics textbook available Econometrics is the quantitative language of economic theory, analysis, and empirical work, and it has become a cornerstone of graduate economics programs. Econometrics provides graduate and PhD students with an essential introduction to this foundational subject in economics and serves as an invaluable reference for researchers and practitioners. This comprehensive textbook teaches fundamental concepts, emphasizes modern, real-world applications, and gives students an intuitive understanding of econometrics. Covers the full breadth of econometric theory and methods with mathematical rigor while emphasizing intuitive explanations that are accessible to students of all backgroundsDraws on integrated, research-level datasets, provided on an accompanying websiteDiscusses linear econometrics, time series, panel data, nonparametric methods, nonlinear econometric models, and modern machine learningFeatures hundreds of exercises that enable students to learn by doingIncludes in-depth appendices on matrix algebra and useful inequalities and a wealth of real-world examplesCan serve as a core textbook for a first-year PhD course in econometrics and as a follow-up to Bruce E. Hansen’s Probability and Statistics for Economists
Author: Viktor Subbotin
Author: Viktor Subbotin
Author: Jonas Böhmer
Author: Jonas Böhmer
Author: Michael R. Chernick
Author: Connie Page
Author: Roger Koenker
Author: David R. Hunter
Author: 
Author: Per K. Andersen
Author: Bruce Hansen