Degenerate U And V Statistics Under Weak Dependence

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Degenerate U- and V-statistics Under Weak Dependence

Author : Anne Leucht
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (846 download)

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Book Synopsis Degenerate U- and V-statistics Under Weak Dependence by : Anne Leucht

Download or read book Degenerate U- and V-statistics Under Weak Dependence written by Anne Leucht and published by . This book was released on 2011 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerous test statistics can be approximated by statistics of U- or V-type. In the case of i.i.d. random variables the limit distribution can be derived by a spectral decomposition of the kernel if the latter is square integrable. To use the same method for dependent data, restrictive assumptions on the associated eigenvalues and eigenfunctions are required. In the majority of cases, it is quite complicated or even impossible to check these conditions. Therefore we employ a wavelet decomposition of the kernel in order to derive the asymptotic distributions of U- and V-statistics for weakly dependent data. This approach only requires some moment constraints and smoothness assumptions concerning the kernel. The asymptotic distributions of U- and V-statistics for both independent and weakly dependent observations cannot be used directly since they depend on certain parameters, which in turn depend on the underlying situation in a complicated way. Therefore, problems arise as soon as critical values for test statistics of U- and V-type have to be determined. The bootstrap offers a convenient way to circumvent these problems, see [3] for the i.i.d. case. We derive the consistency of general bootstrap methods for statistics of weakly dependent data.

Issues in Statistics, Decision Making, and Stochastics: 2013 Edition

Author :
Publisher : ScholarlyEditions
ISBN 13 : 1490110828
Total Pages : 314 pages
Book Rating : 4.4/5 (91 download)

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Book Synopsis Issues in Statistics, Decision Making, and Stochastics: 2013 Edition by :

Download or read book Issues in Statistics, Decision Making, and Stochastics: 2013 Edition written by and published by ScholarlyEditions. This book was released on 2013-05-01 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: Issues in Statistics, Decision Making, and Stochastics: 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about Regular and Chaotic Dynamics. The editors have built Issues in Statistics, Decision Making, and Stochastics: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Regular and Chaotic Dynamics in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Statistics, Decision Making, and Stochastics: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

Asymptotic Laws and Methods in Stochastics

Author : Donald Dawson
Publisher : Springer
ISBN 13 : 1493930761
Total Pages : 401 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Asymptotic Laws and Methods in Stochastics by : Donald Dawson

Download or read book Asymptotic Laws and Methods in Stochastics written by Donald Dawson and published by Springer. This book was released on 2015-11-12 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains articles arising from a conference in honour of mathematician-statistician Miklόs Csörgő on the occasion of his 80th birthday, held in Ottawa in July 2012. It comprises research papers and overview articles, which provide a substantial glimpse of the history and state-of-the-art of the field of asymptotic methods in probability and statistics, written by leading experts. The volume consists of twenty articles on topics on limit theorems for self-normalized processes, planar processes, the central limit theorem and laws of large numbers, change-point problems, short and long range dependent time series, applied probability and stochastic processes, and the theory and methods of statistics. It also includes Csörgő’s list of publications during more than 50 years, since 1962.

Dependence in Probability and Statistics

Author : Patrice Bertail
Publisher : Springer Science & Business Media
ISBN 13 : 038736062X
Total Pages : 491 pages
Book Rating : 4.3/5 (873 download)

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Book Synopsis Dependence in Probability and Statistics by : Patrice Bertail

Download or read book Dependence in Probability and Statistics written by Patrice Bertail and published by Springer Science & Business Media. This book was released on 2006-09-24 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an account of recent developments in the field of probability and statistics for dependent data. It covers a wide range of topics from Markov chain theory and weak dependence with an emphasis on some recent developments on dynamical systems, to strong dependence in times series and random fields. There is a section on statistical estimation problems and specific applications. The book is written as a succession of papers by field specialists, alternating general surveys, mostly at a level accessible to graduate students in probability and statistics, and more general research papers mainly suitable to researchers in the field.

U-Statistics in Banach Spaces

Author : Yu. V. Boroskikh
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 311231395X
Total Pages : 436 pages
Book Rating : 4.1/5 (123 download)

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Book Synopsis U-Statistics in Banach Spaces by : Yu. V. Boroskikh

Download or read book U-Statistics in Banach Spaces written by Yu. V. Boroskikh and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-05-18 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "U-Statistics in Banach Spaces".

Weakly Dependent Stochastic Sequences and Their Applications: Asymptotic statistics based on weakly dependent data

Author : Ken-ichi Yoshihara
Publisher :
ISBN 13 :
Total Pages : 326 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Weakly Dependent Stochastic Sequences and Their Applications: Asymptotic statistics based on weakly dependent data by : Ken-ichi Yoshihara

Download or read book Weakly Dependent Stochastic Sequences and Their Applications: Asymptotic statistics based on weakly dependent data written by Ken-ichi Yoshihara and published by . This book was released on 1992 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Dependence in Probability and Statistics

Author : Paul Doukhan
Publisher : Springer Science & Business Media
ISBN 13 : 3642141048
Total Pages : 222 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Dependence in Probability and Statistics by : Paul Doukhan

Download or read book Dependence in Probability and Statistics written by Paul Doukhan and published by Springer Science & Business Media. This book was released on 2010-07-23 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: This account of recent works on weakly dependent, long memory and multifractal processes introduces new dependence measures for studying complex stochastic systems and includes other topics such as the dependence structure of max-stable processes.

U-Statistics in Banach Spaces

Author : IU. IUrii Vasilevich Borovskikh
Publisher : VSP
ISBN 13 : 9789067642002
Total Pages : 442 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis U-Statistics in Banach Spaces by : IU. IUrii Vasilevich Borovskikh

Download or read book U-Statistics in Banach Spaces written by IU. IUrii Vasilevich Borovskikh and published by VSP. This book was released on 1996-01-01 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: U-statistics are universal objects of modern probabilistic summation theory. They appear in various statistical problems and have very important applications. The mathematical nature of this class of random variables has a functional character and, therefore, leads to the investigation of probabilistic distributions in infinite-dimensional spaces. The situation when the kernel of a U-statistic takes values in a Banach space, turns out to be the most natural and interesting. In this book, the author presents in a systematic form the probabilistic theory of U-statistics with values in Banach spaces (UB-statistics), which has been developed to date. The exposition of the material in this book is based around the following topics: algebraic and martingale properties of U-statistics; inequalities; law of large numbers; the central limit theorem; weak convergence to a Gaussian chaos and multiple stochastic integrals; invariance principle and functional limit theorems; estimates of the rate of weak convergence; asymptotic expansion of distributions; large deviations; law of iterated logarithm; dependent variables; relation between Banach-valued U-statistics and functionals from permanent random measures.

High Dimensional Probability II

Author : Evarist Giné
Publisher : Springer Science & Business Media
ISBN 13 : 1461213584
Total Pages : 491 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis High Dimensional Probability II by : Evarist Giné

Download or read book High Dimensional Probability II written by Evarist Giné and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: High dimensional probability, in the sense that encompasses the topics rep resented in this volume, began about thirty years ago with research in two related areas: limit theorems for sums of independent Banach space valued random vectors and general Gaussian processes. An important feature in these past research studies has been the fact that they highlighted the es sential probabilistic nature of the problems considered. In part, this was because, by working on a general Banach space, one had to discard the extra, and often extraneous, structure imposed by random variables taking values in a Euclidean space, or by processes being indexed by sets in R or Rd. Doing this led to striking advances, particularly in Gaussian process theory. It also led to the creation or introduction of powerful new tools, such as randomization, decoupling, moment and exponential inequalities, chaining, isoperimetry and concentration of measure, which apply to areas well beyond those for which they were created. The general theory of em pirical processes, with its vast applications in statistics, the study of local times of Markov processes, certain problems in harmonic analysis, and the general theory of stochastic processes are just several of the broad areas in which Gaussian process techniques and techniques from probability in Banach spaces have made a substantial impact. Parallel to this work on probability in Banach spaces, classical proba bility and empirical process theory were enriched by the development of powerful results in strong approximations.

Some Extensions of U- and V- Statistics

Author : Shwu-Rong Shieh
Publisher :
ISBN 13 :
Total Pages : 294 pages
Book Rating : 4.:/5 (89 download)

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Book Synopsis Some Extensions of U- and V- Statistics by : Shwu-Rong Shieh

Download or read book Some Extensions of U- and V- Statistics written by Shwu-Rong Shieh and published by . This book was released on 1990 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Multiple Wiener-Ito Integrals

Author : P. Major
Publisher : Springer
ISBN 13 : 3540385576
Total Pages : 134 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Multiple Wiener-Ito Integrals by : P. Major

Download or read book Multiple Wiener-Ito Integrals written by P. Major and published by Springer. This book was released on 2006-11-14 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Empirical Process Techniques for Dependent Data

Author : Herold Dehling
Publisher : Springer Science & Business Media
ISBN 13 : 1461200997
Total Pages : 378 pages
Book Rating : 4.4/5 (612 download)

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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 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,

Harnack's Inequality for Degenerate and Singular Parabolic Equations

Author : Emmanuele DiBenedetto
Publisher : Springer Science & Business Media
ISBN 13 : 1461415845
Total Pages : 287 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Harnack's Inequality for Degenerate and Singular Parabolic Equations by : Emmanuele DiBenedetto

Download or read book Harnack's Inequality for Degenerate and Singular Parabolic Equations written by Emmanuele DiBenedetto and published by Springer Science & Business Media. This book was released on 2011-11-13 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: Degenerate and singular parabolic equations have been the subject of extensive research for the last 25 years. Despite important achievements, the issue of the Harnack inequality for non-negative solutions to these equations, both of p-Laplacian and porous medium type, while raised by several authors, has remained basically open. Recently considerable progress has been made on this issue, to the point that, except for the singular sub-critical range, both for the p-laplacian and the porous medium equations, the theory is reasonably complete. It seemed therefore timely to trace a comprehensive overview, that would highlight the main issues and also the problems that still remain open. The authors give a comprehensive treatment of the Harnack inequality for non-negative solutions to p-laplace and porous medium type equations, both in the degenerate (p/i”2 or im/i”1) and in the singular range (1“ip/i2 or 0“im/i

U-statistics for Detecting and Estimating Changes in Weakly Dependent Functional Data

Author : Lea Wegner
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (139 download)

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Book Synopsis U-statistics for Detecting and Estimating Changes in Weakly Dependent Functional Data by : Lea Wegner

Download or read book U-statistics for Detecting and Estimating Changes in Weakly Dependent Functional Data written by Lea Wegner and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Independent and Stationary Sequences of Random Variables

Author : Ilʹdar Abdulovich Ibragimov
Publisher :
ISBN 13 :
Total Pages : 456 pages
Book Rating : 4.:/5 (44 download)

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Book Synopsis Independent and Stationary Sequences of Random Variables by : Ilʹdar Abdulovich Ibragimov

Download or read book Independent and Stationary Sequences of Random Variables written by Ilʹdar Abdulovich Ibragimov and published by . This book was released on 1971 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Introduction to Empirical Processes and Semiparametric Inference

Author : Michael R. Kosorok
Publisher : Springer Science & Business Media
ISBN 13 : 0387749780
Total Pages : 482 pages
Book Rating : 4.3/5 (877 download)

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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.

Filtration in Porous Media and Industrial Application

Author : M.S. Espedal
Publisher : Springer
ISBN 13 : 3540446567
Total Pages : 225 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Filtration in Porous Media and Industrial Application by : M.S. Espedal

Download or read book Filtration in Porous Media and Industrial Application written by M.S. Espedal and published by Springer. This book was released on 2007-05-06 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the presentation of some flow problems in porous media having relevant industrial applications. The main topics covered are: the manufacturing of composite materials, the espresso coffee brewing process, the filtration of liquids through diapers, various questions about flow problems in oil reservoirs and the theory of homogenization. The aim is to show that filtration problems arising in very practical industrial context exhibit interesting and highly nontrivial mathematical aspects. Thus the style of the book is mathematically rigorous, but specifically oriented towards applications, so that it is intended for both applied mathematicians and researchers in various areas of technological interest. The reader is required to have a good knowledge of the classical theory of PDE and basic functional analysis.