Empirical Process Techniques For Dependent Data
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Empirical Process Techniques For Dependent Data
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Author : Herold Dehling
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Empirical Process Techniques For Dependent Data written by Herold Dehling 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.
Empirical process techniques for independent data have been used for many years in statistics and probability theory. These techniques have proved very useful for studying asymptotic properties of parametric as well as non-parametric statistical procedures. Recently, the need to model the dependence structure in data sets from many different subject areas such as finance, insurance, and telecommunications has led to new developments concerning the empirical distribution function and the empirical process for dependent, mostly stationary sequences. This work gives an introduction to this new theory of empirical process techniques, which has so far been scattered in the statistical and probabilistic literature, and surveys the most recent developments in various related fields. Key features: A thorough and comprehensive introduction to the existing theory of empirical process techniques for dependent data * Accessible surveys by leading experts of the most recent developments in various related fields * Examines empirical process techniques for dependent data, useful for studying parametric and non-parametric statistical procedures * Comprehensive bibliographies * An overview of applications in various fields related to empirical processes: e.g., spectral analysis of time-series, the bootstrap for stationary sequences, extreme value theory, and the empirical process for mixing dependent observations, including the case of strong dependence. To date this book is the only comprehensive treatment of the topic in book literature. It is an ideal introductory text that will serve as a reference or resource for classroom use in the areas of statistics, time-series analysis, extreme value theory, point process theory, and applied probability theory. Contributors: P. Ango Nze, M.A. Arcones, I. Berkes, R. Dahlhaus, J. Dedecker, H.G. Dehling,
Empirical Process Techniques For Dependent Data
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Author : Herold Dehling
language : en
Publisher: Birkhauser
Release Date : 2002-01-01
Empirical Process Techniques For Dependent Data written by Herold Dehling and has been published by Birkhauser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-01 with Estimation theory categories.
Introduction To Empirical Processes And Semiparametric Inference
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Author : Michael R. Kosorok
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-29
Introduction To Empirical Processes And Semiparametric Inference written by Michael R. Kosorok 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 2007-12-29 with Mathematics categories.
The goal of this book is to introduce statisticians, and other researchers with a background in mathematical statistics, to empirical processes and semiparametric inference. These powerful research techniques are surpr- ingly useful for studying large sample properties of statistical estimates from realistically complex models as well as for developing new and - proved approaches to statistical inference. This book is more of a textbook than a research monograph, although a number of new results are presented. The level of the book is more - troductory than the seminal work of van der Vaart and Wellner (1996). In fact, another purpose of this work is to help readers prepare for the mathematically advanced van der Vaart and Wellner text, as well as for the semiparametric inference work of Bickel, Klaassen, Ritov and We- ner (1997). These two books, along with Pollard (1990) and Chapters 19 and 25 of van der Vaart (1998), formulate a very complete and successful elucidation of modern empirical process methods. The present book owes much by the way of inspiration, concept, and notation to these previous works.What is perhaps new is the gradual—yetrigorous—anduni?ed way this book introduces the reader to the ?eld.
Empirical Processes
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Author : David Pollard
language : en
Publisher: IMS
Release Date : 1990
Empirical Processes written by David Pollard and has been published by IMS this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.
Functional Gaussian Approximation For Dependent Structures
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Author : Florence Merlevède
language : en
Publisher: Oxford University Press
Release Date : 2019-02-14
Functional Gaussian Approximation For Dependent Structures written by Florence Merlevède 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 2019-02-14 with Mathematics categories.
Functional Gaussian Approximation for Dependent Structures develops and analyses mathematical models for phenomena that evolve in time and influence each another. It provides a better understanding of the structure and asymptotic behaviour of stochastic processes. Two approaches are taken. Firstly, the authors present tools for dealing with the dependent structures used to obtain normal approximations. Secondly, they apply normal approximations to various examples. The main tools consist of inequalities for dependent sequences of random variables, leading to limit theorems, including the functional central limit theorem and functional moderate deviation principle. The results point out large classes of dependent random variables which satisfy invariance principles, making possible the statistical study of data coming from stochastic processes both with short and long memory. The dependence structures considered throughout the book include the traditional mixing structures, martingale-like structures, and weakly negatively dependent structures, which link the notion of mixing to the notions of association and negative dependence. Several applications are carefully selected to exhibit the importance of the theoretical results. They include random walks in random scenery and determinantal processes. In addition, due to their importance in analysing new data in economics, linear processes with dependent innovations will also be considered and analysed.
Statistical Inference For Discrete Time Stochastic Processes
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Author : M. B. Rajarshi
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-07-08
Statistical Inference For Discrete Time Stochastic Processes written by M. B. Rajarshi 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 2014-07-08 with Mathematics categories.
This work is an overview of statistical inference in stationary, discrete time stochastic processes. Results in the last fifteen years, particularly on non-Gaussian sequences and semi-parametric and non-parametric analysis have been reviewed. The first chapter gives a background of results on martingales and strong mixing sequences, which enable us to generate various classes of CAN estimators in the case of dependent observations. Topics discussed include inference in Markov chains and extension of Markov chains such as Raftery's Mixture Transition Density model and Hidden Markov chains and extensions of ARMA models with a Binomial, Poisson, Geometric, Exponential, Gamma, Weibull, Lognormal, Inverse Gaussian and Cauchy as stationary distributions. It further discusses applications of semi-parametric methods of estimation such as conditional least squares and estimating functions in stochastic models. Construction of confidence intervals based on estimating functions is discussed in some detail. Kernel based estimation of joint density and conditional expectation are also discussed. Bootstrap and other resampling procedures for dependent sequences such as Markov chains, Markov sequences, linear auto-regressive moving average sequences, block based bootstrap for stationary sequences and other block based procedures are also discussed in some detail. This work can be useful for researchers interested in knowing developments in inference in discrete time stochastic processes. It can be used as a material for advanced level research students.
Contemporary Developments In Statistical Theory
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Author : Soumendra Lahiri
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-02
Contemporary Developments In Statistical Theory written by Soumendra Lahiri 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 2013-12-02 with Mathematics categories.
This volume highlights Prof. Hira Koul’s achievements in many areas of Statistics, including Asymptotic theory of statistical inference, Robustness, Weighted empirical processes and their applications, Survival Analysis, Nonlinear time series and Econometrics, among others. Chapters are all original papers that explore the frontiers of these areas and will assist researchers and graduate students working in Statistics, Econometrics and related areas. Prof. Hira Koul was the first Ph.D. student of Prof. Peter Bickel. His distinguished career in Statistics includes the receipt of many prestigious awards, including the Senior Humbolt award (1995), and dedicated service to the profession through editorial work for journals and through leadership roles in professional societies, notably as the past president of the International Indian Statistical Association. Prof. Hira Koul has graduated close to 30 Ph.D. students, and made several seminal contributions in about 125 innovative research papers. The long list of his distinguished collaborators is represented by the contributors to this volume.
Large Sample Techniques For Statistics
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Author : Jiming Jiang
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-06-30
Large Sample Techniques For Statistics written by Jiming Jiang 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 2010-06-30 with Mathematics categories.
In a way, the world is made up of approximations, and surely there is no exception in the world of statistics. In fact, approximations, especially large sample approximations, are very important parts of both theoretical and - plied statistics.TheGaussiandistribution,alsoknownasthe normaldistri- tion,is merelyonesuchexample,dueto thewell-knowncentrallimittheorem. Large-sample techniques provide solutions to many practical problems; they simplify our solutions to di?cult, sometimes intractable problems; they j- tify our solutions; and they guide us to directions of improvements. On the other hand, just because large-sample approximations are used everywhere, and every day, it does not guarantee that they are used properly, and, when the techniques are misused, there may be serious consequences. 2 Example 1 (Asymptotic? distribution). Likelihood ratio test (LRT) is one of the fundamental techniques in statistics. It is well known that, in the 2 “standard” situation, the asymptotic null distribution of the LRT is?,with the degreesoffreedomequaltothe di?erencebetweenthedimensions,de?ned as the numbers of free parameters, of the two nested models being compared (e.g., Rice 1995, pp. 310). This might lead to a wrong impression that the 2 asymptotic (null) distribution of the LRT is always? . A similar mistake 2 might take place when dealing with Pearson’s? -test—the asymptotic distri- 2 2 bution of Pearson’s? -test is not always? (e.g., Moore 1978).
Contemporaneous Event Studies In Corporate Finance
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Author : Jau-Lian Jeng
language : en
Publisher: Springer Nature
Release Date : 2020-11-03
Contemporaneous Event Studies In Corporate Finance written by Jau-Lian Jeng and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-03 with Business & Economics categories.
Providing a comprehensive overview of event study methodology in the field of corporate finance, this book discusses how traditional methods verify the significance and insignificance of events in statistical sampling, and emphasize possible deviation from the statistics of interest. However, the author illustrates the flaws of conventional methodology and proposes alternative methods which can be used for a more robust study of estimating normal and abnormal returns. Traditional methods fail to recognize that the importance of an event will also influence the frequency of the occurrence of the event, and consequently they produce subjective sampling results. This book highlights contemporaneous recursive methods which can be used to track down normal returns and avoid arbitrary determination for the estimation and event period. In addition, the author offers an alternative monitoring scheme to identify the events of concern. Addressing a need for more objective sampling methods in corporate finance event studies, this timely book will appeal to students and academics researching financial econometrics and time series analysis, corporate finance and capital markets.
High Dimensional Probability
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Author : Evarist Giné
language : en
Publisher: IMS
Release Date : 2006
High Dimensional Probability written by Evarist Giné and has been published by IMS this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.