U Statistics In Banach Spaces
DOWNLOAD
Download U Statistics In Banach Spaces PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get U Statistics In Banach Spaces book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
U Statistics In Banach Spaces
DOWNLOAD
Author : IU. IUrii Vasilevich Borovskikh
language : en
Publisher: VSP
Release Date : 1996-01-01
U Statistics In Banach Spaces written by IU. IUrii Vasilevich Borovskikh and has been published by VSP this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-01-01 with Mathematics categories.
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.
U Statistics In Banach Spaces
DOWNLOAD
Author : Yu. V. Borovskikh
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-05-18
U Statistics In Banach Spaces written by Yu. V. Borovskikh and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-18 with Mathematics categories.
No detailed description available for "U-Statistics in Banach Spaces".
Probability In Banach Spaces 8 Proceedings Of The Eighth International Conference
DOWNLOAD
Author : R.M. Dudley
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Probability In Banach Spaces 8 Proceedings Of The Eighth International Conference written by R.M. Dudley and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Probability limit theorems in infinite-dimensional spaces give conditions un der which convergence holds uniformly over an infinite class of sets or functions. Early results in this direction were the Glivenko-Cantelli, Kolmogorov-Smirnov and Donsker theorems for empirical distribution functions. Already in these cases there is convergence in Banach spaces that are not only infinite-dimensional but nonsep arable. But the theory in such spaces developed slowly until the late 1970's. Meanwhile, work on probability in separable Banach spaces, in relation with the geometry of those spaces, began in the 1950's and developed strongly in the 1960's and 70's. We have in mind here also work on sample continuity and boundedness of Gaussian processes and random methods in harmonic analysis. By the mid-70's a substantial theory was in place, including sharp infinite-dimensional limit theorems under either metric entropy or geometric conditions. Then, modern empirical process theory began to develop, where the collection of half-lines in the line has been replaced by much more general collections of sets in and functions on multidimensional spaces. Many of the main ideas from probability in separable Banach spaces turned out to have one or more useful analogues for empirical processes. Tightness became "asymptotic equicontinuity. " Metric entropy remained useful but also was adapted to metric entropy with bracketing, random entropies, and Kolchinskii-Pollard entropy. Even norms themselves were in some situations replaced by measurable majorants, to which the well-developed separable theory then carried over straightforwardly.
A Large Deviation Principle For U Statistics In Banach Spaces
DOWNLOAD
Author : Yuri V. Borovskikh
language : en
Publisher:
Release Date : 1998
A Large Deviation Principle For U Statistics In Banach Spaces written by Yuri V. Borovskikh and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.
Theory Of U Statistics
DOWNLOAD
Author : Vladimir S. Korolyuk
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Theory Of U Statistics written by Vladimir S. Korolyuk and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
The theory of U-statistics goes back to the fundamental work of Hoeffding [1], in which he proved the central limit theorem. During last forty years the interest to this class of random variables has been permanently increasing, and thus, the new intensively developing branch of probability theory has been formed. The U-statistics are one of the universal objects of the modem probability theory of summation. On the one hand, they are more complicated "algebraically" than sums of independent random variables and vectors, and on the other hand, they contain essential elements of dependence which display themselves in the martingale properties. In addition, the U -statistics as an object of mathematical statistics occupy one of the central places in statistical problems. The development of the theory of U-statistics is stipulated by the influence of the classical theory of summation of independent random variables: The law of large num bers, central limit theorem, invariance principle, and the law of the iterated logarithm we re proved, the estimates of convergence rate were obtained, etc.
On The Estimation Of Multiple Random Integrals And U Statistics
DOWNLOAD
Author : Péter Major
language : en
Publisher: Springer
Release Date : 2013-06-28
On The Estimation Of Multiple Random Integrals And U Statistics written by Péter Major and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-28 with Mathematics categories.
This work starts with the study of those limit theorems in probability theory for which classical methods do not work. In many cases some form of linearization can help to solve the problem, because the linearized version is simpler. But in order to apply such a method we have to show that the linearization causes a negligible error. The estimation of this error leads to some important large deviation type problems, and the main subject of this work is their investigation. We provide sharp estimates of the tail distribution of multiple integrals with respect to a normalized empirical measure and so-called degenerate U-statistics and also of the supremum of appropriate classes of such quantities. The proofs apply a number of useful techniques of modern probability that enable us to investigate the non-linear functionals of independent random variables. This lecture note yields insights into these methods, and may also be useful for those who only want some new tools to help them prove limit theorems when standard methods are not a viable option.
U Statistics In Banach Spaces
DOWNLOAD
Author : Yu. V. Boroskikh
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-05-18
U Statistics In Banach Spaces written by Yu. V. Boroskikh and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-18 with Mathematics categories.
No detailed description available for "U-Statistics in Banach Spaces".
High Dimensional Probability Ii
DOWNLOAD
Author : Evarist Giné
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
High Dimensional Probability Ii written by Evarist Giné and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
A Short Course On Banach Space Theory
DOWNLOAD
Author : N. L. Carothers
language : en
Publisher: Cambridge University Press
Release Date : 2005
A Short Course On Banach Space Theory written by N. L. Carothers and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
Publisher Description
Banach Fr Chet Hilbert And Neumann Spaces
DOWNLOAD
Author : Jacques Simon
language : en
Publisher: John Wiley & Sons
Release Date : 2017-05-24
Banach Fr Chet Hilbert And Neumann Spaces written by Jacques Simon and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-24 with Mathematics categories.
This book is the first of a set dedicated to the mathematical tools used in partial differential equations derived from physics. Its focus is on normed or semi-normed vector spaces, including the spaces of Banach, Fréchet and Hilbert, with new developments on Neumann spaces, but also on extractable spaces. The author presents the main properties of these spaces, which are useful for the construction of Lebesgue and Sobolev distributions with real or vector values and for solving partial differential equations. Differential calculus is also extended to semi-normed spaces. Simple methods, semi-norms, sequential properties and others are discussed, making these tools accessible to the greatest number of students – doctoral students, postgraduate students – engineers and researchers without restricting or generalizing the results.