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Author: R. M. Dudley Publisher: Cambridge University Press ISBN: 1107728886 Category : Mathematics Languages : en Pages : 488
Book Description
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.
Author: Oliver Johnson Publisher: World Scientific ISBN: 9781860945373 Category : Computers Languages : en Pages : 230
Book Description
Annotation. - Presents surprising, interesting connections between two apparently separate areas of mathematics- Written by one of the researchers who discovered these connections- Offers a new way of looking at familiar results.
Author: Hans Fischer Publisher: Springer Science & Business Media ISBN: 0387878572 Category : Mathematics Languages : en Pages : 402
Book Description
This study discusses the history of the central limit theorem and related probabilistic limit theorems from about 1810 through 1950. In this context the book also describes the historical development of analytical probability theory and its tools, such as characteristic functions or moments. The central limit theorem was originally deduced by Laplace as a statement about approximations for the distributions of sums of independent random variables within the framework of classical probability, which focused upon specific problems and applications. Making this theorem an autonomous mathematical object was very important for the development of modern probability theory.
Author: Barbara Illowsky Publisher: ISBN: 9781998295470 Category : Business & Economics Languages : en Pages : 0
Book Description
Book Publication Date: Dec 13, 2023. Full color. Introductory Statistics 2e provides an engaging, practical, and thorough overview of the core concepts and skills taught in most one-semester statistics courses. The text focuses on diverse applications from a variety of fields and societal contexts, including business, healthcare, sciences, sociology, political science, computing, and several others. The material supports students with conceptual narratives, detailed step-by-step examples, and a wealth of illustrations, as well as collaborative exercises, technology integration problems, and statistics labs. The text assumes some knowledge of intermediate algebra, and includes thousands of problems and exercises that offer instructors and students ample opportunity to explore and reinforce useful statistical skills.
Author: D. Pollard Publisher: David Pollard ISBN: 0387909907 Category : Mathematics Languages : en Pages : 223
Book Description
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.
Author: Oliver Johnson Publisher: World Scientific ISBN: 1783260610 Category : Mathematics Languages : en Pages : 224
Book Description
This book provides a comprehensive description of a new method of proving the central limit theorem, through the use of apparently unrelated results from information theory. It gives a basic introduction to the concepts of entropy and Fisher information, and collects together standard results concerning their behaviour. It brings together results from a number of research papers as well as unpublished material, showing how the techniques can give a unified view of limit theorems. Contents:Introduction to Information TheoryConvergence in Relative EntropyNon-Identical Variables and Random VectorsDependent Random VariablesConvergence to Stable LawsConvergence on Compact GroupsConvergence to Poisson DistributionFree Random Variables Readership: Graduate students, academics and researchers in probability and statistics. Key Features:Presents surprising, interesting connections between two apparently separate areas of mathematicsWritten by one of the researchers who discovered these connectionsOffers a new way of looking at familiar resultsKeywords:Information Theory;Entropy;Fisher Information;Central Limit Theorem;Probability;Statistics;Convergence of Random VariablesReviews:“This book provides a well-written and motivating introduction to information theory and a detailed description of the current research regarding the connections between central limit theorems and information theory. It is an important reference for many graduate students and researchers in this domain.”Mathematical Reviews
Author: Emmanuel Rio Publisher: Springer ISBN: 3662543230 Category : Mathematics Languages : en Pages : 204
Book Description
Ces notes sont consacrées aux inégalités et aux théorèmes limites classiques pour les suites de variables aléatoires absolument régulières ou fortement mélangeantes au sens de Rosenblatt. Le but poursuivi est de donner des outils techniques pour l'étude des processus faiblement dépendants aux statisticiens ou aux probabilistes travaillant sur ces processus.
Author: L. Saulis Publisher: Springer Science & Business Media ISBN: 9401135304 Category : Mathematics Languages : en Pages : 241
Book Description
"Et moi ... - si j'avait su comment en revenir. One service mathematics has rendered the je n'y serais poin t aile.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O.H ea viside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non Iinearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service. topology has rendered mathematical physics .. .':: 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d 'e1:re of this series
Author: R. M. Dudley
Author: R. M. Dudley
Author: R. M. Dudley
Author: R. M. Dudley
Author: Oliver Johnson
Author: Hans Fischer
Author: Barbara Illowsky
Author: D. Pollard
Author: Oliver Johnson
Author: Emmanuel Rio
Author: L. Saulis