U Statistics

Download or read book U-Statistics written by A J. Lee and published by Routledge. This book was released on 2019-03-13 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book U-Statistics, Mm-Estimators and Resampling written by Arup Bose and published by Springer. This book was released on 2018-08-28 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Modern Applied U-Statistics written by Jeanne Kowalski and published by John Wiley & Sons. This book was released on 2008-01-28 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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 Asymptotic Statistics written by A. W. van der Vaart and published by Cambridge University Press. This book was released on 2000-06-19 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the field of asymptotic statistics. The treatment is both practical and mathematically rigorous. In addition to most of the standard topics of an asymptotics course, including likelihood inference, M-estimation, the theory of asymptotic efficiency, U-statistics, and rank procedures, the book also presents recent research topics such as semiparametric models, the bootstrap, and empirical processes and their applications. The topics are organized from the central idea of approximation by limit experiments, which gives the book one of its unifying themes. This entails mainly the local approximation of the classical i.i.d. set up with smooth parameters by location experiments involving a single, normally distributed observation. Thus, even the standard subjects of asymptotic statistics are presented in a novel way. Suitable as a graduate or Master s level statistics text, this book will also give researchers an overview of the latest research in asymptotic statistics.

Download or read book U Can: Statistics For Dummies written by Deborah J. Rumsey and published by John Wiley & Sons. This book was released on 2015-07-08 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: Make studying statistics simple with this easy-to-read resource Wouldn't it be wonderful if studying statistics were easier? With U Can: Statistics I For Dummies, it is! This one-stop resource combines lessons, practical examples, study questions, and online practice problems to provide you with the ultimate guide to help you score higher in your statistics course. Foundational statistics skills are a must for students of many disciplines, and leveraging study materials such as this one to supplement your statistics course can be a life-saver. Because U Can: Statistics I For Dummies contains both the lessons you need to learn and the practice problems you need to put the concepts into action, you'll breeze through your scheduled study time. Statistics is all about collecting and interpreting data, and is applicable in a wide range of subject areas—which translates into its popularity among students studying in diverse programs. So, if you feel a bit unsure in class, rest assured that there is an easy way to help you grasp the nuances of statistics! Understand statistical ideas, techniques, formulas, and calculations Interpret and critique graphs and charts, determine probability, and work with confidence intervals Critique and analyze data from polls and experiments Combine learning and applying your new knowledge with practical examples, practice problems, and expanded online resources U Can: Statistics I For Dummies contains everything you need to score higher in your fundamental statistics course!

Download or read book Introduction to Probability written by Joseph K. Blitzstein and published by CRC Press. This book was released on 2014-07-24 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developed from celebrated Harvard statistics lectures, Introduction to Probability provides essential language and tools for understanding statistics, randomness, and uncertainty. The book explores a wide variety of applications and examples, ranging from coincidences and paradoxes to Google PageRank and Markov chain Monte Carlo (MCMC). Additional application areas explored include genetics, medicine, computer science, and information theory. The print book version includes a code that provides free access to an eBook version. The authors present the material in an accessible style and motivate concepts using real-world examples. Throughout, they use stories to uncover connections between the fundamental distributions in statistics and conditioning to reduce complicated problems to manageable pieces. The book includes many intuitive explanations, diagrams, and practice problems. Each chapter ends with a section showing how to perform relevant simulations and calculations in R, a free statistical software environment.