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Author: T. L. Lai Publisher: ISBN: Category : Mathematics Languages : en Pages : 560
Book Description
Presents a collection of 18 papers, many of which are surveys, on asymptotic theory in probability and statistics, with applications to a variety of problems. This volume comprises three parts: limit theorems, statistics and applications, and mathematical finance and insurance. It is suitable for graduate students in probability and statistics.
Author: T. L. Lai Publisher: ISBN: Category : Mathematics Languages : en Pages : 560
Book Description
Presents a collection of 18 papers, many of which are surveys, on asymptotic theory in probability and statistics, with applications to a variety of problems. This volume comprises three parts: limit theorems, statistics and applications, and mathematical finance and insurance. It is suitable for graduate students in probability and statistics.
Author: Anirban DasGupta Publisher: Springer Science & Business Media ISBN: 0387759719 Category : Mathematics Languages : en Pages : 727
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: B. L. S. Prakasa Rao Publisher: ISBN: Category : Mathematics Languages : en Pages : 458
Book Description
Probability and stochastic processes; Limit theorems for some statistics; Asymptotic theory of estimation; Linear parametric inference; Martingale approach to inference; Inference in nonlinear regression; Von mises functionals; Empirical characteristic function and its applications.
Author: N. Balakrishnan Publisher: Springer Science & Business Media ISBN: 1461202094 Category : Business & Economics Languages : en Pages : 541
Book Description
Traditions of the 150-year-old St. Petersburg School of Probability and Statis tics had been developed by many prominent scientists including P. L. Cheby chev, A. M. Lyapunov, A. A. Markov, S. N. Bernstein, and Yu. V. Linnik. In 1948, the Chair of Probability and Statistics was established at the Department of Mathematics and Mechanics of the St. Petersburg State University with Yu. V. Linik being its founder and also the first Chair. Nowadays, alumni of this Chair are spread around Russia, Lithuania, France, Germany, Sweden, China, the United States, and Canada. The fiftieth anniversary of this Chair was celebrated by an International Conference, which was held in St. Petersburg from June 24-28, 1998. More than 125 probabilists and statisticians from 18 countries (Azerbaijan, Canada, Finland, France, Germany, Hungary, Israel, Italy, Lithuania, The Netherlands, Norway, Poland, Russia, Taiwan, Turkey, Ukraine, Uzbekistan, and the United States) participated in this International Conference in order to discuss the current state and perspectives of Probability and Mathematical Statistics. The conference was organized jointly by St. Petersburg State University, St. Petersburg branch of Mathematical Institute, and the Euler Institute, and was partially sponsored by the Russian Foundation of Basic Researches. The main theme of the Conference was chosen in the tradition of the St.
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: I.A. Ibragimov Publisher: Springer Science & Business Media ISBN: 1489900276 Category : Mathematics Languages : en Pages : 410
Book Description
when certain parameters in the problem tend to limiting values (for example, when the sample size increases indefinitely, the intensity of the noise ap proaches zero, etc.) To address the problem of asymptotically optimal estimators consider the following important case. Let X 1, X 2, ... , X n be independent observations with the joint probability density !(x,O) (with respect to the Lebesgue measure on the real line) which depends on the unknown patameter o e 9 c R1. It is required to derive the best (asymptotically) estimator 0:( X b ... , X n) of the parameter O. The first question which arises in connection with this problem is how to compare different estimators or, equivalently, how to assess their quality, in terms of the mean square deviation from the parameter or perhaps in some other way. The presently accepted approach to this problem, resulting from A. Wald's contributions, is as follows: introduce a nonnegative function w(0l> ( ), Ob Oe 9 (the loss function) and given two estimators Of and O! n 2 2 the estimator for which the expected loss (risk) Eown(Oj, 0), j = 1 or 2, is smallest is called the better with respect to Wn at point 0 (here EoO is the expectation evaluated under the assumption that the true value of the parameter is 0). Obviously, such a method of comparison is not without its defects.
Author: Masanobu Taniguchi Publisher: Springer Science & Business Media ISBN: 146121162X Category : Mathematics Languages : en Pages : 671
Book Description
The primary aim of this book is to provide modern statistical techniques and theory for stochastic processes. The stochastic processes mentioned here are not restricted to the usual AR, MA, and ARMA processes. A wide variety of stochastic processes, including non-Gaussian linear processes, long-memory processes, nonlinear processes, non-ergodic processes and diffusion processes are described. The authors discuss estimation and testing theory and many other relevant statistical methods and techniques.
Author: A N Shiryaev Publisher: World Scientific ISBN: 9814494151 Category : Mathematics Languages : en Pages : 300
Book Description
This volume provides an exposition of some fundamental aspects of the asymptotic theory of statistical experiments. The most important of them is “how to construct asymptotically optimal decisions if we know the structure of optimal decisions for the limit experiment”. Contents:Statistical Experiments and Their ComparisonConvergence of Statistical Experiments(γ,Γ)-Models. Convergence to (γ,Γ)-ModelsLocal Convergence of Statistical Experiments and Global EstimationStatistical Inference for Autoregressive Models of the First Order Readership: Researchers in probability and statistics. Keywords:Comparison of Statistical Experiments;Mixed Local Asymptotic Normality;Convergence of Experiments;Likelihood Ratio Processes;Contiguity;Autoregressive Models;Minimax Bound;Local Asymptotic NormalityReviews: “It is an interesting, welcome addition to the literature, and it contains many new insights. I congratulate the authors for writing this comprehensive monograph on a difficult subject.” Mathematical Reviews “The book is a highlight in modern mathematical statistics which offers a lot of new concepts. It recalls the brilliant methodology of Le Cam's Theory and the first chapters may be used as introduction into this field.” Mathematics Abstracts
Author: T. L. Lai
Author: T. L. Lai
Author: Anirban DasGupta
Author: B. L. S. Prakasa Rao
Author: N. Balakrishnan
Author: A. W. van der Vaart
Author: Brendan McCabe
Author: I.A. Ibragimov
Author: János Galambos
Author: Masanobu Taniguchi
Author: A N Shiryaev