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Statistical Estimation Asymptotic Theory
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Book Synopsis Statistical Estimation by : I.A. Ibragimov
Download or read book Statistical Estimation written by I.A. Ibragimov and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Statistical Estimation--asymptotic Theory by : Ilʹdar Abdulovich Ibragimov
Download or read book Statistical Estimation--asymptotic Theory written by Ilʹdar Abdulovich Ibragimov and published by . This book was released on 1981-01-01 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Asymptotic Theory of Statistical Inference for Time Series by : Masanobu Taniguchi
Download or read book Asymptotic Theory of Statistical Inference for Time Series written by Masanobu Taniguchi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 671 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Asymptotic Theory of Statistical Inference by : B. L. S. Prakasa Rao
Download or read book Asymptotic Theory of Statistical Inference written by B. L. S. Prakasa Rao and published by . This book was released on 1987-01-16 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Asymptotic Statistics by : A. W. van der Vaart
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.
Book Synopsis Asymptotic Theory of Statistics and Probability by : Anirban DasGupta
Download or read book Asymptotic Theory of Statistics and Probability written by Anirban DasGupta and published by Springer Science & Business Media. This book was released on 2008-03-07 with total page 726 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Asymptotic Theory Of Quantum Statistical Inference: Selected Papers by : Masahito Hayashi
Download or read book Asymptotic Theory Of Quantum Statistical Inference: Selected Papers written by Masahito Hayashi and published by World Scientific. This book was released on 2005-02-21 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum statistical inference, a research field with deep roots in the foundations of both quantum physics and mathematical statistics, has made remarkable progress since 1990. In particular, its asymptotic theory has been developed during this period. However, there has hitherto been no book covering this remarkable progress after 1990; the famous textbooks by Holevo and Helstrom deal only with research results in the earlier stage (1960s-1970s).This book presents the important and recent results of quantum statistical inference. It focuses on the asymptotic theory, which is one of the central issues of mathematical statistics and had not been investigated in quantum statistical inference until the early 1980s. It contains outstanding papers after Holevo's textbook, some of which are of great importance but are not available now.The reader is expected to have only elementary mathematical knowledge, and therefore much of the content will be accessible to graduate students as well as research workers in related fields. Introductions to quantum statistical inference have been specially written for the book. Asymptotic Theory of Quantum Statistical Inference: Selected Papers will give the reader a new insight into physics and statistical inference.
Book Synopsis Asymptotic Theory of Statistical Estimation in Non-regular Cases by :
Download or read book Asymptotic Theory of Statistical Estimation in Non-regular Cases written by and published by . This book was released on 1979 with total page 67 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Asymptotic Theory of Statistical Estimation by : Masafumi Akahira
Download or read book Asymptotic Theory of Statistical Estimation written by Masafumi Akahira and published by . This book was released on 1991 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Asymptotic theory of statistical estimation in non-regular cases by : Masafumi Akahira
Download or read book Asymptotic theory of statistical estimation in non-regular cases written by Masafumi Akahira and published by . This book was released on 1979 with total page 67 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Robust Asymptotic Statistics by : Helmut Rieder
Download or read book Robust Asymptotic Statistics written by Helmut Rieder and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1 To the king, my lord, from your servant Balasi : 2 ... The king should have a look. Maybe the scribe who reads to the king did not understand . . . . shall I personally show, with this tablet that I am sending to the king, my lord, how the omen was written. 3 Really, he who has not followed the text with his finger cannot possibly understand it. This book is about optimally robust functionals and their unbiased esti mators and tests. Functionals extend the parameter of the assumed ideal center model to neighborhoods of this model that contain the actual distri bution. The two principal questions are (F): Which functional to choose? and (P): Which statistical procedure to use for the selected functional? Using a local asymptotic framework, we deal with both problems by linking up nonparametric statistical optimality with infinitesimal robust ness criteria. Thus, seemingly separate developments in robust statistics are presented in a unifying way.
Book Synopsis Asymptotic Efficiency of Statistical Estimators: Concepts and Higher Order Asymptotic Efficiency by : Masafumi Akahira
Download or read book Asymptotic Efficiency of Statistical Estimators: Concepts and Higher Order Asymptotic Efficiency written by Masafumi Akahira and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is a collection of results recently obtained by the authors. Most of these have been published, while others are awaitlng publication. Our investigation has two main purposes. Firstly, we discuss higher order asymptotic efficiency of estimators in regular situa tions. In these situations it is known that the maximum likelihood estimator (MLE) is asymptotically efficient in some (not always specified) sense. However, there exists here a whole class of asymptotically efficient estimators which are thus asymptotically equivalent to the MLE. It is required to make finer distinctions among the estimators, by considering higher order terms in the expansions of their asymptotic distributions. Secondly, we discuss asymptotically efficient estimators in non regular situations. These are situations where the MLE or other estimators are not asymptotically normally distributed, or where l 2 their order of convergence (or consistency) is not n / , as in the regular cases. It is necessary to redefine the concept of asympto tic efficiency, together with the concept of the maximum order of consistency. Under the new definition as asymptotically efficient estimator may not always exist. We have not attempted to tell the whole story in a systematic way. The field of asymptotic theory in statistical estimation is relatively uncultivated. So, we have tried to focus attention on such aspects of our recent results which throw light on the area.
Book Synopsis Statistical Experiments And Decision, Asymptotic Theory by : Albert N Shiryaev
Download or read book Statistical Experiments And Decision, Asymptotic Theory written by Albert N Shiryaev and published by World Scientific. This book was released on 2000-07-04 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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”.
Book Synopsis Asymptotic Theory for Solutions in Statistical Estimation and Stochastic Programming by : International Business Machines Corporation. Research Division
Download or read book Asymptotic Theory for Solutions in Statistical Estimation and Stochastic Programming written by International Business Machines Corporation. Research Division and published by . This book was released on 1991 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Asymptotic Efficiency of Statistical Estimators: Concepts and Higher Order Asymptotic Efficiency by : Masafumi Akahira
Download or read book Asymptotic Efficiency of Statistical Estimators: Concepts and Higher Order Asymptotic Efficiency written by Masafumi Akahira and published by Springer. This book was released on 2011-11-22 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is a collection of results recently obtained by the authors. Most of these have been published, while others are awaitlng publication. Our investigation has two main purposes. Firstly, we discuss higher order asymptotic efficiency of estimators in regular situa tions. In these situations it is known that the maximum likelihood estimator (MLE) is asymptotically efficient in some (not always specified) sense. However, there exists here a whole class of asymptotically efficient estimators which are thus asymptotically equivalent to the MLE. It is required to make finer distinctions among the estimators, by considering higher order terms in the expansions of their asymptotic distributions. Secondly, we discuss asymptotically efficient estimators in non regular situations. These are situations where the MLE or other estimators are not asymptotically normally distributed, or where l 2 their order of convergence (or consistency) is not n / , as in the regular cases. It is necessary to redefine the concept of asympto tic efficiency, together with the concept of the maximum order of consistency. Under the new definition as asymptotically efficient estimator may not always exist. We have not attempted to tell the whole story in a systematic way. The field of asymptotic theory in statistical estimation is relatively uncultivated. So, we have tried to focus attention on such aspects of our recent results which throw light on the area.
Book Synopsis Statistical Experiments and Decisions by : Al?bert Nikolaevich Shiri?aev
Download or read book Statistical Experiments and Decisions written by Al?bert Nikolaevich Shiri?aev and published by World Scientific. This book was released on 2000 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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?.
Book Synopsis Asymptotic Theory of statistical tests and estimation by : Indra Mohan Chakravarti
Download or read book Asymptotic Theory of statistical tests and estimation written by Indra Mohan Chakravarti and published by . This book was released on 1980 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
