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 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 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 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 Theory of Spatial Statistics written by M.N.M. van Lieshout and published by CRC Press. This book was released on 2019-03-19 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theory of Spatial Statistics: A Concise Introduction presents the most important models used in spatial statistics, including random fields and point processes, from a rigorous mathematical point of view and shows how to carry out statistical inference. It contains full proofs, real-life examples and theoretical exercises. Solutions to the latter are available in an appendix. Assuming maturity in probability and statistics, these concise lecture notes are self-contained and cover enough material for a semester course. They may also serve as a reference book for researchers. Features * Presents the mathematical foundations of spatial statistics. * Contains worked examples from mining, disease mapping, forestry, soil and environmental science, and criminology. * Gives pointers to the literature to facilitate further study. * Provides example code in R to encourage the student to experiment. * Offers exercises and their solutions to test and deepen understanding. The book is suitable for postgraduate and advanced undergraduate students in mathematics and statistics.
Download or read book Elements of Large Sample Theory written by E.L. Lehmann and published by Springer Science & Business Media. This book was released on 2006-04-18 with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by one of the main figures in twentieth century statistics, this book provides a unified treatment of first-order large-sample theory. It discusses a broad range of applications including introductions to density estimation, the bootstrap, and the asymptotics of survey methodology. The book is written at an elementary level making it accessible to most readers.
Download or read book Statistical Models written by David A. Freedman and published by Cambridge University Press. This book was released on 2009-04-27 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: This lively and engaging book explains the things you have to know in order to read empirical papers in the social and health sciences, as well as the techniques you need to build statistical models of your own. The discussion in the book is organized around published studies, as are many of the exercises. Relevant journal articles are reprinted at the back of the book. Freedman makes a thorough appraisal of the statistical methods in these papers and in a variety of other examples. He illustrates the principles of modelling, and the pitfalls. The discussion shows you how to think about the critical issues - including the connection (or lack of it) between the statistical models and the real phenomena. The book is written for advanced undergraduates and beginning graduate students in statistics, as well as students and professionals in the social and health sciences.
Download or read book written by and published by . This book was released on 2007 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Theory of Statistics written by Mark J. Schervish and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 732 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this graduate textbook is to provide a comprehensive advanced course in the theory of statistics covering those topics in estimation, testing, and large sample theory which a graduate student might typically need to learn as preparation for work on a Ph.D. An important strength of this book is that it provides a mathematically rigorous and even-handed account of both Classical and Bayesian inference in order to give readers a broad perspective. For example, the "uniformly most powerful" approach to testing is contrasted with available decision-theoretic approaches.
Download or read book Theory U written by C. Otto Scharmer and published by Berrett-Koehler Publishers. This book was released on 2009-01-01 with total page 891 pages. Available in PDF, EPUB and Kindle. Book excerpt: Shows how leaders can access the deepest source of inspiration and vision • Includes dozens of tested exercises, practices, and real-world examples We live in a time of massive institutional failure, one that requires a new consciousness and a new collective leadership capacity. In this groundbreaking book, Otto Scharmer invites us to see the world in new ways and in so doing discover a revolutionary approach to leadership. What we pay attention to and how we pay attention is key to what we create. What prevents us from attending to situations more effectively is that we aren’t fully aware of and in touch with the inner place from which attention and intention originate. This is what Scharmer calls our blind spot. By moving through Scharmer’s U process, we consciously access the blind spot and learn to connect to our authentic Self—the deepest source of knowledge and inspiration—in the realm of “presencing,” a term coined by Scharmer that combines the concepts of presence and sensing. Based on ten years of research and action learning and interviews with over 150 practitioners and thought leaders, Theory U offers a rich diversity of compelling stories and examples and includes dozens of exercises and practices that allow leaders, and entire organizations, to shift awareness, connect with the best future possibility, and gain the ability to realize it.
Download or read book All of Statistics written by Larry Wasserman and published by Springer Science & Business Media. This book was released on 2013-12-11 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Taken literally, the title "All of Statistics" is an exaggeration. But in spirit, the title is apt, as the book does cover a much broader range of topics than a typical introductory book on mathematical statistics. This book is for people who want to learn probability and statistics quickly. It is suitable for graduate or advanced undergraduate students in computer science, mathematics, statistics, and related disciplines. The book includes modern topics like non-parametric curve estimation, bootstrapping, and classification, topics that are usually relegated to follow-up courses. The reader is presumed to know calculus and a little linear algebra. No previous knowledge of probability and statistics is required. Statistics, data mining, and machine learning are all concerned with collecting and analysing data.
Download or read book Theory and Methods of Statistics written by P.K. Bhattacharya and published by Academic Press. This book was released on 2016-06-23 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theory and Methods of Statistics covers essential topics for advanced graduate students and professional research statisticians. This comprehensive resource covers many important areas in one manageable volume, including core subjects such as probability theory, mathematical statistics, and linear models, and various special topics, including nonparametrics, curve estimation, multivariate analysis, time series, and resampling. The book presents subjects such as "maximum likelihood and sufficiency," and is written with an intuitive, heuristic approach to build reader comprehension. It also includes many probability inequalities that are not only useful in the context of this text, but also as a resource for investigating convergence of statistical procedures. Codifies foundational information in many core areas of statistics into a comprehensive and definitive resource Serves as an excellent text for select master’s and PhD programs, as well as a professional reference Integrates numerous examples to illustrate advanced concepts Includes many probability inequalities useful for investigating convergence of statistical procedures
Download or read book Probability and Statistics written by Michael J. Evans and published by Macmillan. This book was released on 2004 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unlike traditional introductory math/stat textbooks, Probability and Statistics: The Science of Uncertainty brings a modern flavor based on incorporating the computer to the course and an integrated approach to inference. From the start the book integrates simulations into its theoretical coverage, and emphasizes the use of computer-powered computation throughout.* Math and science majors with just one year of calculus can use this text and experience a refreshing blend of applications and theory that goes beyond merely mastering the technicalities. They'll get a thorough grounding in probability theory, and go beyond that to the theory of statistical inference and its applications. An integrated approach to inference is presented that includes the frequency approach as well as Bayesian methodology. Bayesian inference is developed as a logical extension of likelihood methods. A separate chapter is devoted to the important topic of model checking and this is applied in the context of the standard applied statistical techniques. Examples of data analyses using real-world data are presented throughout the text. A final chapter introduces a number of the most important stochastic process models using elementary methods. *Note: An appendix in the book contains Minitab code for more involved computations. The code can be used by students as templates for their own calculations. If a software package like Minitab is used with the course then no programming is required by the students.
Download or read book Probability Statistics and Truth written by Richard Von Mises and published by Courier Corporation. This book was released on 1981-01-01 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive study of probability considers the approaches of Pascal, Laplace, Poisson, and others. It also discusses Laws of Large Numbers, the theory of errors, and other relevant topics.
Download or read book A Course in Large Sample Theory written by Thomas S. Ferguson and published by Routledge. This book was released on 2017-09-06 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Course in Large Sample Theory is presented in four parts. The first treats basic probabilistic notions, the second features the basic statistical tools for expanding the theory, the third contains special topics as applications of the general theory, and the fourth covers more standard statistical topics. Nearly all topics are covered in their multivariate setting.The book is intended as a first year graduate course in large sample theory for statisticians. It has been used by graduate students in statistics, biostatistics, mathematics, and related fields. Throughout the book there are many examples and exercises with solutions. It is an ideal text for self study.
Download or read book Probability Theory written by Yuan S. Chow and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt: Apart from new examples and exercises, some simplifications of proofs, minor improvements, and correction of typographical errors, the principal change from the first edition is the addition of section 9.5, dealing with the central limit theorem for martingales and more general stochastic arrays. vii Preface to the First Edition Probability theory is a branch of mathematics dealing with chance phenomena and has clearly discernible links with the real world. The origins of the sub ject, generally attributed to investigations by the renowned French mathe matician Fermat of problems posed by a gambling contemporary to Pascal, have been pushed back a century earlier to the Italian mathematicians Cardano and Tartaglia about 1570 (Ore, 1953). Results as significant as the Bernoulli weak law of large numbers appeared as early as 1713, although its counterpart, the Borel strong law oflarge numbers, did not emerge until 1909. Central limit theorems and conditional probabilities were already being investigated in the eighteenth century, but the first serious attempts to grapple with the logical foundations of probability seem to be Keynes (1921), von Mises (1928; 1931), and Kolmogorov (1933).
Download or read book Problems in Probability Theory Mathematical Statistics and Theory of Random Functions written by A. A. Sveshnikov and published by Courier Corporation. This book was released on 2012-04-30 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approximately 1,000 problems — with answers and solutions included at the back of the book — illustrate such topics as random events, random variables, limit theorems, Markov processes, and much more.
