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Uniform Central Limit Theorems

Author: R. M. Dudley
Publisher: Cambridge University Press
ISBN: 0521461022
Size: 69.23 MB
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This treatise by an acknowledged expert includes several topics not found in any previous book.

Uniform Central Limit Theorems

Author: R. M. Dudley
Publisher: Cambridge University Press
ISBN: 1107728886
Size: 32.50 MB
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In this new edition of a classic work on empirical processes the author, an acknowledged expert, gives a thorough treatment of the subject with the addition of several proved theorems not included in the first edition, including the Bretagnolle–Massart theorem giving constants in the Komlos–Major–Tusnady rate of convergence for the classical empirical process, Massart's form of the Dvoretzky–Kiefer–Wolfowitz inequality with precise constant, Talagrand's generic chaining approach to boundedness of Gaussian processes, a characterization of uniform Glivenko–Cantelli classes of functions, Giné and Zinn's characterization of uniform Donsker classes, and the Bousquet–Koltchinskii–Panchenko theorem that the convex hull of a uniform Donsker class is uniform Donsker. The book will be an essential reference for mathematicians working in infinite-dimensional central limit theorems, mathematical statisticians, and computer scientists working in computer learning theory. Problems are included at the end of each chapter so the book can also be used as an advanced text.

Advanced Lectures On Machine Learning

Author: Shahar Mendelson
Publisher: Springer Science & Business Media
ISBN: 3540005293
Size: 74.69 MB
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This book presents revised reviewed versions of lectures given during the Machine Learning Summer School held in Canberra, Australia, in February 2002. The lectures address the following key topics in algorithmic learning: statistical learning theory, kernel methods, boosting, reinforcement learning, theory learning, association rule learning, and learning linear classifier systems. Thus, the book is well balanced between classical topics and new approaches in machine learning. Advanced students and lecturers will find this book a coherent in-depth overview of this exciting area, while researchers will use this book as a valuable source of reference.

Real Analysis And Probability

Author: R. M. Dudley
Publisher: CRC Press
ISBN: 135108464X
Size: 63.94 MB
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Written by one of the best-known probabilists in the world this text offers a clear and modern presentation of modern probability theory and an exposition of the interplay between the properties of metric spaces and those of probability measures. This text is the first at this level to include discussions of the subadditive ergodic theorems, metrics for convergence in laws and the Borel isomorphism theory. The proofs for the theorems are consistently brief and clear and each chapter concludes with a set of historical notes and references. This book should be of interest to students taking degree courses in real analysis and/or probability theory.

Unit Roots Cointegration And Structural Change

Author: G. S. Maddala
Publisher: Cambridge University Press
ISBN: 9780521587822
Size: 11.99 MB
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Time series analysis has undergone many changes in recent years with the advent of unit roots and cointegration. Maddala and Kim present a comprehensive review of these important developments and examine structural change. The volume provides an analysis of unit root tests, problems with unit root testing, estimation of cointegration systems, cointegration tests, and econometric estimation with integrated regressors. The authors also present the Bayesian approach to these problems and bootstrap methods for small-sample inference. The chapters on structural change discuss the problems of unit root tests and cointegration under structural change, outliers and robust methods, the Markov-switching model and Harvey's structural time series model. Unit Roots, Cointegration and Structural Change is a major contribution to Themes in Modern Econometrics, of interest both to specialists and graduate and upper-undergraduate students.

Martingale Limit Theory And Its Application

Author: P. Hall
Publisher: Academic Press
ISBN: 1483263223
Size: 54.90 MB
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Martingale Limit Theory and Its Application discusses the asymptotic properties of martingales, particularly as regards key prototype of probabilistic behavior that has wide applications. The book explains the thesis that martingale theory is central to probability theory, and also examines the relationships between martingales and processes embeddable in or approximated by Brownian motion. The text reviews the martingale convergence theorem, the classical limit theory and analogs, and the martingale limit theorems viewed as the rate of convergence results in the martingale convergence theorem. The book explains the square function inequalities, weak law of large numbers, as well as the strong law of large numbers. The text discusses the reverse martingales, martingale tail sums, the invariance principles in the central limit theorem, and also the law of the iterated logarithm. The book investigates the limit theory for stationary processes via corresponding results for approximating martingales and the estimation of parameters from stochastic processes. The text can be profitably used as a reference for mathematicians, advanced students, and professors of higher mathematics or statistics.

Subsampling

Author: Dimitris N. Politis
Publisher: Springer Science & Business Media
ISBN: 1461215544
Size: 68.36 MB
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Since Efron's profound paper on the bootstrap, an enormous amount of effort has been spent on the development of bootstrap, jacknife, and other resampling methods. The primary goal of these computer-intensive methods has been to provide statistical tools that work in complex situations without imposing unrealistic or unverifiable assumptions about the data generating mechanism. This book sets out to lay some of the foundations for subsampling methodology and related methods.

Markov Processes Gaussian Processes And Local Times

Author: Michael B. Marcus
Publisher: Cambridge University Press
ISBN: 1139458833
Size: 11.12 MB
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This book was first published in 2006. Written by two of the foremost researchers in the field, this book studies the local times of Markov processes by employing isomorphism theorems that relate them to certain associated Gaussian processes. It builds to this material through self-contained but harmonized 'mini-courses' on the relevant ingredients, which assume only knowledge of measure-theoretic probability. The streamlined selection of topics creates an easy entrance for students and experts in related fields. The book starts by developing the fundamentals of Markov process theory and then of Gaussian process theory, including sample path properties. It then proceeds to more advanced results, bringing the reader to the heart of contemporary research. It presents the remarkable isomorphism theorems of Dynkin and Eisenbaum and then shows how they can be applied to obtain new properties of Markov processes by using well-established techniques in Gaussian process theory. This original, readable book will appeal to both researchers and advanced graduate students.

Probability

Author: Rick Durrett
Publisher: Cambridge University Press
ISBN: 113949113X
Size: 45.93 MB
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This classic introduction to probability theory for beginning graduate students covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications. Its philosophy is that the best way to learn probability is to see it in action, so there are 200 examples and 450 problems. The fourth edition begins with a short chapter on measure theory to orient readers new to the subject.