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.
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 Asymptotic Methods in Statistical Decision Theory written by Lucien Le Cam and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 767 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book grew out of lectures delivered at the University of California, Berkeley, over many years. The subject is a part of asymptotics in statistics, organized around a few central ideas. The presentation proceeds from the general to the particular since this seemed the best way to emphasize the basic concepts. The reader is expected to have been exposed to statistical thinking and methodology, as expounded for instance in the book by H. Cramer [1946] or the more recent text by P. Bickel and K. Doksum [1977]. Another pos sibility, closer to the present in spirit, is Ferguson [1967]. Otherwise the reader is expected to possess some mathematical maturity, but not really a great deal of detailed mathematical knowledge. Very few mathematical objects are used; their assumed properties are simple; the results are almost always immediate consequences of the definitions. Some objects, such as vector lattices, may not have been included in the standard background of a student of statistics. For these we have provided a summary of relevant facts in the Appendix. The basic structures in the whole affair are systems that Blackwell called "experiments" and "transitions" between them. An "experiment" is a mathe matical abstraction intended to describe the basic features of an observational process if that process is contemplated in advance of its implementation. Typically, an experiment consists of a set E> of theories about what may happen in the observational process.
Download or read book Asymptotic Efficiency of Nonparametric Tests written by I︠A︡kov I︠U︡rʹevich Nikitin and published by Cambridge University Press. This book was released on 1995-06-30 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Making a substantiated choice of the most efficient statistical test is one of the basic problems of statistics. Asymptotic efficiency is an indispensable technique for comparing and ordering statistical tests in large samples. It is especially useful in nonparametric statistics where it is usually necessary to rely on heuristic tests. This monograph presents a unified treatment of the analysis and calculation of the asymptotic efficiencies of nonparametric tests. Powerful new methods are developed to evaluate explicitly different kinds of efficiencies. Of particular interest is the description of domains of the Bahadur local optimality and related characterisation problems based on recent research by the author. Other Russian results are also published here for the first time in English. Researchers, professionals and students in statistics will find this book invaluable.
Download or read book Statistical Tests Of Nonparametric Hypotheses Asymptotic Theory written by Odile Pons and published by World Scientific. This book was released on 2013-10-04 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: An overview of the asymptotic theory of optimal nonparametric tests is presented in this book. It covers a wide range of topics: Neyman-Pearson and LeCam's theories of optimal tests, the theories of empirical processes and kernel estimators with extensions of their applications to the asymptotic behavior of tests for distribution functions, densities and curves of the nonparametric models defining the distributions of point processes and diffusions. With many new test statistics developed for smooth curves, the reliance on kernel estimators with bias corrections and the weak convergence of the estimators are useful to prove the asymptotic properties of the tests, extending the coverage to semiparametric models. They include tests built from continuously observed processes and observations with cumulative intervals.
Download or read book Information Theory and Statistics written by Solomon Kullback and published by Courier Corporation. This book was released on 2012-09-11 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: Highly useful text studies logarithmic measures of information and their application to testing statistical hypotheses. Includes numerous worked examples and problems. References. Glossary. Appendix. 1968 2nd, revised edition.
Download or read book From Finite Sample to Asymptotic Methods in Statistics written by Pranab K. Sen and published by Cambridge University Press. This book was released on 2010 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: A broad view of exact statistical inference and the development of asymptotic statistical inference.
Download or read book An Author and Permuted Title Index to Selected Statistical Journals written by Brian L. Joiner and published by . This book was released on 1970 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: All articles, notes, queries, corrigenda, and obituaries appearing in the following journals during the indicated years are indexed: Annals of mathematical statistics, 1961-1969; Biometrics, 1965-1969#3; Biometrics, 1951-1969; Journal of the American Statistical Association, 1956-1969; Journal of the Royal Statistical Society, Series B, 1954-1969,#2; South African statistical journal, 1967-1969,#2; Technometrics, 1959-1969.--p.iv.
Download or read book Expansions and Asymptotics for Statistics written by Christopher G. Small and published by CRC Press. This book was released on 2010-05-07 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotic methods provide important tools for approximating and analysing functions that arise in probability and statistics. Moreover, the conclusions of asymptotic analysis often supplement the conclusions obtained by numerical methods. Providing a broad toolkit of analytical methods, Expansions and Asymptotics for Statistics shows how asymptoti
Download or read book Library of Congress Subject Headings written by Library of Congress and published by . This book was released on 1996 with total page 1430 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Joint Statistical Papers of Akahira and Takeuchi written by Masafumi Akahira and published by World Scientific. This book was released on 2003 with total page 615 pages. Available in PDF, EPUB and Kindle. Book excerpt: Masafumi Akahira and Kei Takeuchi have collaborated in research on mathematical statistics for nearly thirty years and have published many articles and papers. This volume is a collection of their papers, some published in well-known and others in lesser-known journals. The papers cover various fields, but the main subject is the theory of estimation -- asymptotic, non-regular, sequential, etc. All the papers are theoretical in nature, but have implications for applied problems.
Download or read book Library of Congress Subject Headings written by Library of Congress. Cataloging Policy and Support Office and published by . This book was released on 2007 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Library of Congress Subject Headings A E written by Library of Congress. Subject Cataloging Division and published by . This book was released on 1989 with total page 1468 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Library of Congress Subject Headings written by Library of Congress. Office for Subject Cataloging Policy and published by . This book was released on 1992 with total page 1282 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Encyclopedia of Statistical Sciences Volume 3 written by and published by John Wiley & Sons. This book was released on 2005-12-16 with total page 706 pages. Available in PDF, EPUB and Kindle. Book excerpt: ENCYCLOPEDIA OF STATISTICAL SCIENCES
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.
Download or read book Library of Congress Subject Headings written by Library of Congress. Subject Cataloging Division and published by Washington, D.C. : Cataloging Distribution Service, Library of Congress. This book was released on 1988 with total page 1348 pages. Available in PDF, EPUB and Kindle. Book excerpt:
