U Statistics

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U Statistics

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Author : Lee
language : en
Publisher: CRC Press
Release Date : 1990-06-12

U Statistics written by Lee and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-06-12 with Mathematics categories.

In 1946 Paul Halmos studied unbiased estimators of minimum variance, and planted the seed from which the subject matter of the present monograph sprang. The author has undertaken to provide experts and advanced students with a review of the present status of the evolved theory of U-statistics, and

Theory Of U Statistics

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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.

U Statistics

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Author : A. J. Lee
language : en
Publisher: Routledge
Release Date : 2019-03-13

U Statistics written by A. J. Lee and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-13 with Mathematics categories.

In 1946 Paul Halmos studied unbiased estimators of minimum variance, and planted the seed from which the subject matter of the present monograph sprang. The author has undertaken to provide experts and advanced students with a review of the present status of the evolved theory of U-statistics, including applications to indicate the range and scope of U-statistic methods. Complete with over 200 end-of-chapter references, this is an invaluable addition to the libraries of applied and theoretical statisticians and mathematicians.

Modern Applied U Statistics

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Author : Jeanne Kowalski
language : en
Publisher: John Wiley & Sons
Release Date : 2008-02-13

Modern Applied U Statistics written by Jeanne Kowalski 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 2008-02-13 with Mathematics categories.

A timely and applied approach to the newly discovered methods and applications of U-statistics Built on years of collaborative research and academic experience, Modern Applied U-Statistics successfully presents a thorough introduction to the theory of U-statistics using in-depth examples and applications that address contemporary areas of study including biomedical and psychosocial research. Utilizing a "learn by example" approach, this book provides an accessible, yet in-depth, treatment of U-statistics, as well as addresses key concepts in asymptotic theory by integrating translational and cross-disciplinary research. The authors begin with an introduction of the essential and theoretical foundations of U-statistics such as the notion of convergence in probability and distribution, basic convergence results, stochastic Os, inference theory, generalized estimating equations, as well as the definition and asymptotic properties of U-statistics. With an emphasis on nonparametric applications when and where applicable, the authors then build upon this established foundation in order to equip readers with the knowledge needed to understand the modern-day extensions of U-statistics that are explored in subsequent chapters. Additional topical coverage includes: Longitudinal data modeling with missing data Parametric and distribution-free mixed-effect and structural equation models A new multi-response based regression framework for non-parametric statistics such as the product moment correlation, Kendall's tau, and Mann-Whitney-Wilcoxon rank tests A new class of U-statistic-based estimating equations (UBEE) for dependent responses Motivating examples, in-depth illustrations of statistical and model-building concepts, and an extensive discussion of longitudinal study designs strengthen the real-world utility and comprehension of this book. An accompanying Web site features SAS? and S-Plus? program codes, software applications, and additional study data. Modern Applied U-Statistics accommodates second- and third-year students of biostatistics at the graduate level and also serves as an excellent self-study for practitioners in the fields of bioinformatics and psychosocial research.

Asymptotic Theory Of Statistics And Probability

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Author : Anirban DasGupta
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-03-07

Asymptotic Theory Of Statistics And Probability written by Anirban DasGupta 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 2008-03-07 with Mathematics categories.

This unique book delivers an encyclopedic treatment of classic as well as contemporary large sample theory, dealing with both statistical problems and probabilistic issues and tools. The book is unique in its detailed coverage of fundamental topics. It is written in an extremely lucid style, with an emphasis on the conceptual discussion of the importance of a problem and the impact and relevance of the theorems. There is no other book in large sample theory that matches this book in coverage, exercises and examples, bibliography, and lucid conceptual discussion of issues and theorems.

Probability And Statistical Models With Applications

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Author : CH. A. Charalambides
language : en
Publisher: CRC Press
Release Date : 2000-09-21

Probability And Statistical Models With Applications written by CH. A. Charalambides and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-09-21 with Mathematics categories.

This monograph of carefully collected articles reviews recent developments in theoretical and applied statistical science, highlights current noteworthy results and illustrates their applications; and points out possible new directions to pursue. With its enlightening account of statistical discoveries and its numerous figures and tables, Probabili

U Statistics Mm Estimators And Resampling

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Author : Arup Bose
language : en
Publisher: Springer
Release Date : 2018-08-28

U Statistics Mm Estimators And Resampling written by Arup Bose and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-28 with Mathematics categories.

This is an introductory text on a broad class of statistical estimators that are minimizers of convex functions. It covers the basics of U-statistics and Mm-estimators and develops their asymptotic properties. It also provides an elementary introduction to resampling, particularly in the context of these estimators. The last chapter is on practical implementation of the methods presented in other chapters, using the free software R.

The Energy Of Data And Distance Correlation

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Author : Gábor J. Székely
language : en
Publisher: CRC Press
Release Date : 2023-02-15

The Energy Of Data And Distance Correlation written by Gábor J. Székely and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-15 with Mathematics categories.

Energy distance is a statistical distance between the distributions of random vectors, which characterizes equality of distributions. The name energy derives from Newton's gravitational potential energy, and there is an elegant relation to the notion of potential energy between statistical observations. Energy statistics are functions of distances between statistical observations in metric spaces. The authors hope this book will spark the interest of most statisticians who so far have not explored E-statistics and would like to apply these new methods using R. The Energy of Data and Distance Correlation is intended for teachers and students looking for dedicated material on energy statistics, but can serve as a supplement to a wide range of courses and areas, such as Monte Carlo methods, U-statistics or V-statistics, measures of multivariate dependence, goodness-of-fit tests, nonparametric methods and distance based methods. •E-statistics provides powerful methods to deal with problems in multivariate inference and analysis. •Methods are implemented in R, and readers can immediately apply them using the freely available energy package for R. •The proposed book will provide an overview of the existing state-of-the-art in development of energy statistics and an overview of applications. •Background and literature review is valuable for anyone considering further research or application in energy statistics.

On The Estimation Of Multiple Random Integrals And U Statistics

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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

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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.