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Author: Vladimir S. Korolyuk Publisher: Springer Science & Business Media ISBN: 9401735158 Category : Mathematics Languages : en Pages : 558
Book Description
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.
Author: Vladimir S. Korolyuk Publisher: Springer Science & Business Media ISBN: 9401735158 Category : Mathematics Languages : en Pages : 558
Book Description
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.
Author: A J. Lee Publisher: Routledge ISBN: 1351405853 Category : Mathematics Languages : en Pages : 324
Book Description
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.
Author: A. W. van der Vaart Publisher: Cambridge University Press ISBN: 9780521784504 Category : Mathematics Languages : en Pages : 470
Book Description
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.
Author: C. Otto Scharmer Publisher: Berrett-Koehler Publishers ISBN: 1605099074 Category : Business & Economics Languages : en Pages : 891
Book Description
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.
Author: P.K. Bhattacharya Publisher: Academic Press ISBN: 0128041234 Category : Mathematics Languages : en Pages : 546
Book Description
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
Author: Larry Wasserman Publisher: Springer Science & Business Media ISBN: 0387217363 Category : Mathematics Languages : en Pages : 446
Book Description
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.
Author: A. A. Sveshnikov Publisher: Courier Corporation ISBN: 0486137562 Category : Mathematics Languages : en Pages : 516
Book Description
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.
Author: Anirban DasGupta Publisher: Springer Science & Business Media ISBN: 0387759700 Category : Mathematics Languages : en Pages : 726
Book Description
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.
Author: E.L. Lehmann Publisher: Springer Science & Business Media ISBN: 0387227296 Category : Mathematics Languages : en Pages : 640
Book Description
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.
Author: Mark J. Schervish Publisher: Springer Science & Business Media ISBN: 1461242509 Category : Mathematics Languages : en Pages : 732
Book Description
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.
Author: Vladimir S. Korolyuk
Author: Vladimir S. Korolyuk
Author: A J. Lee
Author: A. W. van der Vaart
Author: C. Otto Scharmer
Author: P.K. Bhattacharya
Author: Larry Wasserman
Author: A. A. Sveshnikov
Author: Anirban DasGupta
Author: E.L. Lehmann
Author: Mark J. Schervish