On The Asymptotic Theory Of Statistical Experiments And Some Of Its Applications PDF Download
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Author | : Al?bert Nikolaevich Shiri?aev |
Publisher | : World Scientific |
Total Pages | : 306 |
Release | : 2000 |
Genre | : Mathematics |
ISBN | : 9789810241018 |
Download Statistical Experiments and Decisions Book in PDF, ePub and Kindle
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?.
Author | : Mohamed W. Moussatat |
Publisher | : |
Total Pages | : 193 |
Release | : 1981 |
Genre | : |
ISBN | : |
Download On the asymptotic theory of statistical experiments and some of its applications Book in PDF, ePub and Kindle
Author | : Mohamed Walid Moussatat |
Publisher | : |
Total Pages | : 410 |
Release | : 1976 |
Genre | : |
ISBN | : |
Download On the Asymptotic Theory of Statistical Experiments and Some of Its Applications Book in PDF, ePub and Kindle
Author | : I.A. Ibragimov |
Publisher | : Springer Science & Business Media |
Total Pages | : 410 |
Release | : 2013-11-11 |
Genre | : Mathematics |
ISBN | : 1489900276 |
Download Statistical Estimation Book in PDF, ePub and Kindle
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 | : Lucien Le Cam |
Publisher | : Springer Science & Business Media |
Total Pages | : 767 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461249465 |
Download Asymptotic Methods in Statistical Decision Theory Book in PDF, ePub and Kindle
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.
Author | : Vladimir G. Spokojnyj |
Publisher | : |
Total Pages | : 281 |
Release | : 1994 |
Genre | : |
ISBN | : |
Download Statistical Experiments and Decisions Book in PDF, ePub and Kindle
Author | : Vladimir E. Bening |
Publisher | : VSP |
Total Pages | : 312 |
Release | : 2000-01-01 |
Genre | : Mathematics |
ISBN | : 9789067643238 |
Download Asymptotic Theory of Testing Statistical Hypotheses Book in PDF, ePub and Kindle
The series is devoted to the publication of high-level monographs and surveys which cover the whole spectrum of probability and statistics. The books of the series are addressed to both experts and advanced students.
Author | : Brendan McCabe |
Publisher | : Manchester University Press |
Total Pages | : 338 |
Release | : 1993 |
Genre | : Estimation theory |
ISBN | : 9780719030536 |
Download Elements of Modern Asymptotic Theory with Statistical Applications Book in PDF, ePub and Kindle
Author | : Masahito Hayashi |
Publisher | : World Scientific |
Total Pages | : 553 |
Release | : 2005-02-21 |
Genre | : Science |
ISBN | : 981448198X |
Download Asymptotic Theory Of Quantum Statistical Inference: Selected Papers Book in PDF, ePub and Kindle
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.
Author | : A. W. van der Vaart |
Publisher | : Cambridge University Press |
Total Pages | : 470 |
Release | : 2000-06-19 |
Genre | : Mathematics |
ISBN | : 9780521784504 |
Download Asymptotic Statistics Book in PDF, ePub and Kindle
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.