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.
Download or read book U Statistics in Banach Spaces written by Yu. V. Borovskikh 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".
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".
Download or read book Probability in Banach Spaces 8 Proceedings of the Eighth International Conference written by R.M. Dudley and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Theory of U Statistics written by Vladimir S. Korolyuk and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 558 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book On the Estimation of Multiple Random Integrals and U Statistics written by Péter Major and published by Springer. This book was released on 2013-06-28 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Large Deviation Principle for U statistics in Banach Spaces written by Yuri V. Borovskikh and published by . This book was released on 1998 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Lectures on Probability Theory and Statistics written by Evarist Giné and published by Springer. This book was released on 2006-11-14 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nur Contents aufnehmen
Download or read book Introduction to Banach Spaces Analysis and Probability written by Daniel Li and published by Cambridge University Press. This book was released on 2018 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second volume of a two-volume overview focuses on the applications of Banach spaces and recent developments in the field.
Download or read book Decoupling written by Victor de la Peña and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: A friendly and systematic introduction to the theory and applications. The book begins with the sums of independent random variables and vectors, with maximal inequalities and sharp estimates on moments, which are later used to develop and interpret decoupling inequalities. Decoupling is first introduced as it applies to randomly stopped processes and unbiased estimation. The authors then proceed with the theory of decoupling in full generality, paying special attention to comparison and interplay between martingale and decoupling theory, and to applications. These include limit theorems, moment and exponential inequalities for martingales and more general dependence structures, biostatistical implications, and moment convergence in Anscombe's theorem and Wald's equation for U--statistics. Addressed to researchers in probability and statistics and to graduates, the expositon is at the level of a second graduate probability course, with a good portion of the material fit for use in a first year course.
Download or read book Martingale Approximation written by Yu. V. Borovskikh and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-01-14 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "Martingale Approximation".
Download or read book Random Permanents written by Yu. V. Borovskikh and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-05-18 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "Random Permanents".
Download or read book Statistical Methods and Practice written by N. Balakrishnan and published by Alpha Science Int'l Ltd.. This book was released on 2003 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chiefly papers presented at the Symposium; festschrift for K.N. Ponnuswamy, b. 1940, and K. Suresh Chandra, b. 1940, Indian statisticians.
Download or read book Probability Theory and Mathematical Statistics written by B. Grigelionis and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-05-18 with total page 752 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "Probability Theory and Mathematical Statistics".
Download or read book Modern Nonparametric Robust and Multivariate Methods written by Klaus Nordhausen and published by Springer. This book was released on 2015-10-05 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by leading experts in the field, this edited volume brings together the latest findings in the area of nonparametric, robust and multivariate statistical methods. The individual contributions cover a wide variety of topics ranging from univariate nonparametric methods to robust methods for complex data structures. Some examples from statistical signal processing are also given. The volume is dedicated to Hannu Oja on the occasion of his 65th birthday and is intended for researchers as well as PhD students with a good knowledge of statistics.
Download or read book A Short Course on Banach Space Theory written by N. L. Carothers and published by Cambridge University Press. This book was released on 2005 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publisher Description
