Empirical Processes with Applications to Statistics

Empirical Processes with Applications to Statistics PDF

Author: Galen R. Shorack

Publisher: SIAM

Published: 2009-01-01

Total Pages: 992

ISBN-13: 0898719011

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Originally published in 1986, this valuable reference provides a detailed treatment of limit theorems and inequalities for empirical processes of real-valued random variables; applications of the theory to censored data, spacings, rank statistics, quantiles, and many functionals of empirical processes, including a treatment of bootstrap methods; and a summary of inequalities that are useful for proving limit theorems. At the end of the Errata section, the authors have supplied references to solutions for 11 of the 19 Open Questions provided in the book's original edition. Audience: researchers in statistical theory, probability theory, biostatistics, econometrics, and computer science.

Introduction to Empirical Processes and Semiparametric Inference

Introduction to Empirical Processes and Semiparametric Inference PDF

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.

Empirical Process Techniques for Dependent Data

Empirical Process Techniques for Dependent Data PDF

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,

Weighted Empirical Processes in Dynamic Nonlinear Models

Weighted Empirical Processes in Dynamic Nonlinear Models PDF

Author: Hira L. Koul

Publisher: Springer Science & Business Media

Published: 2002-06-13

Total Pages: 454

ISBN-13: 9780387954769

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This book presents a unified approach for obtaining the limiting distributions of minimum distance. It discusses classes of goodness-of-t tests for fitting an error distribution in some of these models and/or fitting a regression-autoregressive function without assuming the knowledge of the error distribution. The main tool is the asymptotic equi-continuity of certain basic weighted residual empirical processes in the uniform and L2 metrics.

Convergence of Stochastic Processes

Convergence of Stochastic Processes PDF

Author: D. Pollard

Publisher: David Pollard

Published: 1984-10-08

Total Pages: 223

ISBN-13: 0387909907

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Functionals on stochastic processes; Uniform convergence of empirical measures; Convergence in distribution in euclidean spaces; Convergence in distribution in metric spaces; The uniform metric on space of cadlag functions; The skorohod metric on D [0, oo); Central limit teorems; Martingales.

Contemporary Empirical Methods in Software Engineering

Contemporary Empirical Methods in Software Engineering PDF

Author: Michael Felderer

Publisher: Springer Nature

Published: 2020-08-27

Total Pages: 525

ISBN-13: 3030324893

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This book presents contemporary empirical methods in software engineering related to the plurality of research methodologies, human factors, data collection and processing, aggregation and synthesis of evidence, and impact of software engineering research. The individual chapters discuss methods that impact the current evolution of empirical software engineering and form the backbone of future research. Following an introductory chapter that outlines the background of and developments in empirical software engineering over the last 50 years and provides an overview of the subsequent contributions, the remainder of the book is divided into four parts: Study Strategies (including e.g. guidelines for surveys or design science); Data Collection, Production, and Analysis (highlighting approaches from e.g. data science, biometric measurement, and simulation-based studies); Knowledge Acquisition and Aggregation (highlighting literature research, threats to validity, and evidence aggregation); and Knowledge Transfer (discussing open science and knowledge transfer with industry). Empirical methods like experimentation have become a powerful means of advancing the field of software engineering by providing scientific evidence on software development, operation, and maintenance, but also by supporting practitioners in their decision-making and learning processes. Thus the book is equally suitable for academics aiming to expand the field and for industrial researchers and practitioners looking for novel ways to check the validity of their assumptions and experiences. Chapter 17 is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

Weak Convergence and Empirical Processes

Weak Convergence and Empirical Processes PDF

Author: Aad van der vaart

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 523

ISBN-13: 1475725450

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This book explores weak convergence theory and empirical processes and their applications to many applications in statistics. Part one reviews stochastic convergence in its various forms. Part two offers the theory of empirical processes in a form accessible to statisticians and probabilists. Part three covers a range of topics demonstrating the applicability of the theory to key questions such as measures of goodness of fit and the bootstrap.

Weak Convergence and Empirical Processes

Weak Convergence and Empirical Processes PDF

Author: A. W. van der Vaart

Publisher: Springer Nature

Published: 2023-07-11

Total Pages: 693

ISBN-13: 3031290402

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This book provides an account of weak convergence theory, empirical processes, and their application to a wide variety of problems in statistics. The first part of the book presents a thorough treatment of stochastic convergence in its various forms. Part 2 brings together the theory of empirical processes in a form accessible to statisticians and probabilists. In Part 3, the authors cover a range of applications in statistics including rates of convergence of estimators; limit theorems for M− and Z−estimators; the bootstrap; the functional delta-method and semiparametric estimation. Most of the chapters conclude with “problems and complements.” Some of these are exercises to help the reader’s understanding of the material, whereas others are intended to supplement the text. This second edition includes many of the new developments in the field since publication of the first edition in 1996: Glivenko-Cantelli preservation theorems; new bounds on expectations of suprema of empirical processes; new bounds on covering numbers for various function classes; generic chaining; definitive versions of concentration bounds; and new applications in statistics including penalized M-estimation, the lasso, classification, and support vector machines. The approximately 200 additional pages also round out classical subjects, including chapters on weak convergence in Skorokhod space, on stable convergence, and on processes based on pseudo-observations.

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