Empirical Process Techniques for Dependent Data

Empirical Process Techniques for Dependent Data

Author: Herold Dehling

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 378

ISBN-13: 1461200997

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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,


Book Synopsis Empirical Process Techniques for Dependent Data by : Herold Dehling

Download or read book Empirical Process Techniques for Dependent Data written by Herold Dehling and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Empirical Process Techniques for Dependent Data

Author: Herold Dehling

Publisher: Birkhauser

Published: 2002-01-01

Total Pages: 381

ISBN-13: 9783764342012

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Book Synopsis Empirical Process Techniques for Dependent Data by : Herold Dehling

Download or read book Empirical Process Techniques for Dependent Data written by Herold Dehling and published by Birkhauser. This book was released on 2002-01-01 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Introduction to Empirical Processes and Semiparametric Inference

Introduction to Empirical Processes and Semiparametric Inference

Author: Michael R. Kosorok

Publisher: Springer Science & Business Media

Published: 2007-12-29

Total Pages: 482

ISBN-13: 0387749780

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Kosorok’s brilliant text provides a self-contained introduction to empirical processes and semiparametric inference. These powerful research techniques are surprisingly useful for developing methods of statistical inference for complex models and in understanding the properties of such methods. This is an authoritative text that covers all the bases, and also a friendly and gradual introduction to the area. The book can be used as research reference and textbook.


Book Synopsis Introduction to Empirical Processes and Semiparametric Inference by : Michael R. Kosorok

Download or read book Introduction to Empirical Processes and Semiparametric Inference written by Michael R. Kosorok and published by Springer Science & Business Media. This book was released on 2007-12-29 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kosorok’s brilliant text provides a self-contained introduction to empirical processes and semiparametric inference. These powerful research techniques are surprisingly useful for developing methods of statistical inference for complex models and in understanding the properties of such methods. This is an authoritative text that covers all the bases, and also a friendly and gradual introduction to the area. The book can be used as research reference and textbook.

Empirical Processes

Empirical Processes

Author: David Pollard

Publisher: IMS

Published: 1990

Total Pages: 100

ISBN-13: 9780940600164

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Book Synopsis Empirical Processes by : David Pollard

Download or read book Empirical Processes written by David Pollard and published by IMS. This book was released on 1990 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:

High-Dimensional Probability

High-Dimensional Probability

Author: Roman Vershynin

Publisher: Cambridge University Press

Published: 2018-09-27

Total Pages: 299

ISBN-13: 1108415199

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An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.


Book Synopsis High-Dimensional Probability by : Roman Vershynin

Download or read book High-Dimensional Probability written by Roman Vershynin and published by Cambridge University Press. This book was released on 2018-09-27 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.

Oracle Inequalities in Empirical Risk Minimization and Sparse Recovery Problems

Oracle Inequalities in Empirical Risk Minimization and Sparse Recovery Problems

Author: Vladimir Koltchinskii

Publisher: Springer

Published: 2011-07-29

Total Pages: 259

ISBN-13: 3642221475

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The purpose of these lecture notes is to provide an introduction to the general theory of empirical risk minimization with an emphasis on excess risk bounds and oracle inequalities in penalized problems. In recent years, there have been new developments in this area motivated by the study of new classes of methods in machine learning such as large margin classification methods (boosting, kernel machines). The main probabilistic tools involved in the analysis of these problems are concentration and deviation inequalities by Talagrand along with other methods of empirical processes theory (symmetrization inequalities, contraction inequality for Rademacher sums, entropy and generic chaining bounds). Sparse recovery based on l_1-type penalization and low rank matrix recovery based on the nuclear norm penalization are other active areas of research, where the main problems can be stated in the framework of penalized empirical risk minimization, and concentration inequalities and empirical processes tools have proved to be very useful.


Book Synopsis Oracle Inequalities in Empirical Risk Minimization and Sparse Recovery Problems by : Vladimir Koltchinskii

Download or read book Oracle Inequalities in Empirical Risk Minimization and Sparse Recovery Problems written by Vladimir Koltchinskii and published by Springer. This book was released on 2011-07-29 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of these lecture notes is to provide an introduction to the general theory of empirical risk minimization with an emphasis on excess risk bounds and oracle inequalities in penalized problems. In recent years, there have been new developments in this area motivated by the study of new classes of methods in machine learning such as large margin classification methods (boosting, kernel machines). The main probabilistic tools involved in the analysis of these problems are concentration and deviation inequalities by Talagrand along with other methods of empirical processes theory (symmetrization inequalities, contraction inequality for Rademacher sums, entropy and generic chaining bounds). Sparse recovery based on l_1-type penalization and low rank matrix recovery based on the nuclear norm penalization are other active areas of research, where the main problems can be stated in the framework of penalized empirical risk minimization, and concentration inequalities and empirical processes tools have proved to be very useful.

Functional Gaussian Approximation for Dependent Structures

Functional Gaussian Approximation for Dependent Structures

Author: Florence Merlevède

Publisher: Oxford University Press

Published: 2019-02-14

Total Pages: 496

ISBN-13: 0192561863

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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.


Book Synopsis Functional Gaussian Approximation for Dependent Structures by : Florence Merlevède

Download or read book Functional Gaussian Approximation for Dependent Structures written by Florence Merlevède and published by Oxford University Press. This book was released on 2019-02-14 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Statistical Inference for Discrete Time Stochastic Processes

Author: M. B. Rajarshi

Publisher: Springer Science & Business Media

Published: 2014-07-08

Total Pages: 121

ISBN-13: 8132207637

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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.


Book Synopsis Statistical Inference for Discrete Time Stochastic Processes by : M. B. Rajarshi

Download or read book Statistical Inference for Discrete Time Stochastic Processes written by M. B. Rajarshi and published by Springer Science & Business Media. This book was released on 2014-07-08 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Weak Convergence of Stochastic Processes

Weak Convergence of Stochastic Processes

Author: Vidyadhar S. Mandrekar

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2016-09-26

Total Pages: 148

ISBN-13: 3110475456

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The purpose of this book is to present results on the subject of weak convergence in function spaces to study invariance principles in statistical applications to dependent random variables, U-statistics, censor data analysis. Different techniques, formerly available only in a broad range of literature, are for the first time presented here in a self-contained fashion. Contents: Weak convergence of stochastic processes Weak convergence in metric spaces Weak convergence on C[0, 1] and D[0,∞) Central limit theorem for semi-martingales and applications Central limit theorems for dependent random variables Empirical process Bibliography


Book Synopsis Weak Convergence of Stochastic Processes by : Vidyadhar S. Mandrekar

Download or read book Weak Convergence of Stochastic Processes written by Vidyadhar S. Mandrekar and published by Walter de Gruyter GmbH & Co KG. This book was released on 2016-09-26 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to present results on the subject of weak convergence in function spaces to study invariance principles in statistical applications to dependent random variables, U-statistics, censor data analysis. Different techniques, formerly available only in a broad range of literature, are for the first time presented here in a self-contained fashion. Contents: Weak convergence of stochastic processes Weak convergence in metric spaces Weak convergence on C[0, 1] and D[0,∞) Central limit theorem for semi-martingales and applications Central limit theorems for dependent random variables Empirical process Bibliography

Contemporary Developments in Statistical Theory

Contemporary Developments in Statistical Theory

Author: Soumendra Lahiri

Publisher: Springer Science & Business Media

Published: 2013-12-02

Total Pages: 395

ISBN-13: 3319026518

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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.


Book Synopsis Contemporary Developments in Statistical Theory by : Soumendra Lahiri

Download or read book Contemporary Developments in Statistical Theory written by Soumendra Lahiri and published by Springer Science & Business Media. This book was released on 2013-12-02 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.