Non Regular Statistical Estimation Ii

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Non Regular Statistical Estimation

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Author : Masafumi Akahira
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Non Regular Statistical Estimation written by Masafumi Akahira and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

In order to obtain many of the classical results in the theory of statistical estimation, it is usual to impose regularity conditions on the distributions under consideration. In small sample and large sample theories of estimation there are well established sets of regularity conditions, and it is worth while to examine what may follow if any one of these regularity conditions fail to hold. "Non-regular estimation" literally means the theory of statistical estimation when some or other of the regularity conditions fail to hold. In this monograph, the authors present a systematic study of the meaning and implications of regularity conditions, and show how the relaxation of such conditions can often lead to surprising conclusions. Their emphasis is on considering small sample results and to show how pathological examples may be considered in this broader framework.

Statistical Inference For Non Regular Family Of Distributions Unified Theory

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Author : Milind B. Bhatt
language : en
Publisher: Lulu.com
Release Date :

Statistical Inference For Non Regular Family Of Distributions Unified Theory written by Milind B. Bhatt and has been published by Lulu.com this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

Statistical Estimation

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Author : I.A. Ibragimov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11

Statistical Estimation written by I.A. Ibragimov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.

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.

Selected Papers On Probability And Statistics

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Author :
language : en
Publisher: American Mathematical Soc.
Release Date : 2009

Selected Papers On Probability And Statistics written by and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.

This volume contains translations of papers that originally appeared in the Japanese journal Sugaku. The papers range over a variety of topics in probability theory, statistics, and applications. This volume is suitable for graduate students and research mathematicians interested in probability and statistics.

Statistical Estimation For Truncated Exponential Families

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Author : Masafumi Akahira
language : en
Publisher: Springer
Release Date : 2017-07-26

Statistical Estimation For Truncated Exponential Families written by Masafumi Akahira and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-26 with Mathematics categories.

This book presents new findings on nonregular statistical estimation. Unlike other books on this topic, its major emphasis is on helping readers understand the meaning and implications of both regularity and irregularity through a certain family of distributions. In particular, it focuses on a truncated exponential family of distributions with a natural parameter and truncation parameter as a typical nonregular family. This focus includes the (truncated) Pareto distribution, which is widely used in various fields such as finance, physics, hydrology, geology, astronomy, and other disciplines. The family is essential in that it links both regular and nonregular distributions, as it becomes a regular exponential family if the truncation parameter is known. The emphasis is on presenting new results on the maximum likelihood estimation of a natural parameter or truncation parameter if one of them is a nuisance parameter. In order to obtain more information on the truncation, the Bayesian approach is also considered. Further, the application to some useful truncated distributions is discussed. The illustrated clarification of the nonregular structure provides researchers and practitioners with a solid basis for further research and applications.

An Author And Permuted Title Index To Selected Statistical Journals

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Author : Brian L. Joiner
language : en
Publisher:
Release Date : 1970

An Author And Permuted Title Index To Selected Statistical Journals written by Brian L. Joiner and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Annals of mathematical statistics categories.

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.

Mathematical Statistics

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Author : Johann Pfanzagl
language : en
Publisher: Springer
Release Date : 2017-10-23

Mathematical Statistics written by Johann Pfanzagl and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-23 with Mathematics categories.

This book presents a detailed description of the development of statistical theory. In the mid twentieth century, the development of mathematical statistics underwent an enduring change, due to the advent of more refined mathematical tools. New concepts like sufficiency, superefficiency, adaptivity etc. motivated scholars to reflect upon the interpretation of mathematical concepts in terms of their real-world relevance. Questions concerning the optimality of estimators, for instance, had remained unanswered for decades, because a meaningful concept of optimality (based on the regularity of the estimators, the representation of their limit distribution and assertions about their concentration by means of Anderson’s Theorem) was not yet available. The rapidly developing asymptotic theory provided approximate answers to questions for which non-asymptotic theory had found no satisfying solutions. In four engaging essays, this book presents a detailed description of how the use of mathematical methods stimulated the development of a statistical theory. Primarily focused on methodology, questionable proofs and neglected questions of priority, the book offers an intriguing resource for researchers in theoretical statistics, and can also serve as a textbook for advanced courses in statisticc.

Mathematical Theory Of Bayesian Statistics

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Author : Sumio Watanabe
language : en
Publisher: CRC Press
Release Date : 2018-04-27

Mathematical Theory Of Bayesian Statistics written by Sumio Watanabe and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-27 with Mathematics categories.

Mathematical Theory of Bayesian Statistics introduces the mathematical foundation of Bayesian inference which is well-known to be more accurate in many real-world problems than the maximum likelihood method. Recent research has uncovered several mathematical laws in Bayesian statistics, by which both the generalization loss and the marginal likelihood are estimated even if the posterior distribution cannot be approximated by any normal distribution. Features Explains Bayesian inference not subjectively but objectively. Provides a mathematical framework for conventional Bayesian theorems. Introduces and proves new theorems. Cross validation and information criteria of Bayesian statistics are studied from the mathematical point of view. Illustrates applications to several statistical problems, for example, model selection, hyperparameter optimization, and hypothesis tests. This book provides basic introductions for students, researchers, and users of Bayesian statistics, as well as applied mathematicians. Author Sumio Watanabe is a professor of Department of Mathematical and Computing Science at Tokyo Institute of Technology. He studies the relationship between algebraic geometry and mathematical statistics.

Mathematical Methods Of Statistics

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Author : Harald Cramér
language : en
Publisher: Princeton University Press
Release Date : 2016-06-02

Mathematical Methods Of Statistics written by Harald Cramér and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-02 with Mathematics categories.

Harald Cramér’s classic synthesis of statistical mathematical theory—an invaluable resource for students and practitioners alike In the 1930s, as British and American statisticians were developing the science of statistical inference, French and Russian probabilitists transformed the classical calculus of probability into a rigorous and pure mathematical theory. In this incisive and authoritative book, Harald Cramér unites these two major lines of development, providing a masterly exposition of the mathematical methods of modern statistics that set the standard in the field still followed today. Requiring only a working knowledge of undergraduate mathematics, this self-contained book begins with an introduction to the fundamental concept of a distribution and of integration with respect to a distribution. It goes on to discuss the general theory of random variables and probability distributions, the theory of sampling, statistical estimation, and tests of significance. Blending lucid and accessible writing with mathematical rigor, Mathematical Methods of Statistics belongs on the shelf of anyone interested in statistical methods and remains the standard reference on the subject today.

Oar Cumulative Index Of Research Results

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Author :
language : en
Publisher:
Release Date : 1967

Oar Cumulative Index Of Research Results written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Aeronautics categories.