Contributions To A General Asymptotic Statistical Theory
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Contributions To A General Asymptotic Statistical Theory
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Author : J. Pfanzagl
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Contributions To A General Asymptotic Statistical Theory written by J. Pfanzagl 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.
Contributions To A General Asymptotic Statistical Theory
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Author : W. Wefelmeyer
language : en
Publisher:
Release Date : 1982-11-01
Contributions To A General Asymptotic Statistical Theory written by W. Wefelmeyer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982-11-01 with categories.
Asymptotic Expansions For General Statistical Models
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Author : Johann Pfanzagl
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-27
Asymptotic Expansions For General Statistical Models written by Johann Pfanzagl 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 2013-11-27 with Mathematics categories.
0.1. The aim of the book Our "Contributions to a General Asymptotic Statistical Theory" (Springer Lecture Notes in Statistics, Vol. 13, 1982, called "Vol. I" in the following) suggest to describe the local structure of a general family ~ of probability measures by its tangent space, and the local behavior of a functional K: ~ ~~k by its gradient. Starting from these basic concepts, asymptotic envelope power functions for tests and asymptotic bounds for the concentration of estimators are obtained, and heuristic procedures are suggested for the construction of test- and estimator-sequences attaining these bounds. In the present volume, these asymptotic investigations are carried one step further: From approximations by limit distributions to approximations by Edgeworth expansions, 1 2 adding one term (of order n- / ) to the limit distribution. As in Vol. I, the investigation is "general" in the sense of dealing with arbitrary families of probability measures and arbitrary functionals. The investigation is special in the sense that it is restricted to statistical procedures based on independent, identically distributed observations. 2 Moreover, it is special in the sense that its concern are "regular" models (i.e. families of probability measures and functionals which are subject to certain general conditions, like differentiability). Irregular models are certainly of mathematical interest. Since they are hardly of any practical relevance, it appears justifiable to exclude them at this stage of the investigation.
Statistical Experiments And Decisions
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Author : A N Shiryaev
language : en
Publisher: World Scientific
Release Date : 2000-07-04
Statistical Experiments And Decisions written by A N Shiryaev and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-07-04 with Mathematics categories.
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
Robust Asymptotic Statistics
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Author : Helmut Rieder
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Robust Asymptotic Statistics written by Helmut Rieder 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.
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.
Asymptotic Statistics
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Author : A. W. van der Vaart
language : en
Publisher: Cambridge University Press
Release Date : 2000-06-19
Asymptotic Statistics written by A. W. van der Vaart and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-06-19 with Mathematics categories.
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 research in asymptotic statistics.
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.
Inference Asymptotics And Applications
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Author : Nancy Reid
language : en
Publisher: World Scientific
Release Date : 2017-03-10
Inference Asymptotics And Applications written by Nancy Reid and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-10 with Mathematics categories.
This book showcases the innovative research of Professor Skovgaard, by providing in one place a selection of his most important and influential papers. Introductions by colleagues set in context the highlights, key achievements, and impact, of each work. This book provides a survey of the field of asymptotic theory and inference as it was being pushed forward during an exceptionally fruitful time. It provides students and researchers with an overview of many aspects of the field.
Statistical Experiments And Decisions
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Author : Al?bert Nikolaevich Shiri?aev
language : en
Publisher: World Scientific
Release Date : 2000
Statistical Experiments And Decisions written by Al?bert Nikolaevich Shiri?aev and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
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?.
Higher Order Asymptotic Theory For Time Series Analysis
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Author : Masanobu Taniguchi
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Higher Order Asymptotic Theory For Time Series Analysis written by Masanobu Taniguchi 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.
The initial basis of this book was a series of my research papers, that I listed in References. I have many people to thank for the book's existence. Regarding higher order asymptotic efficiency I thank Professors Kei Takeuchi and M. Akahira for their many comments. I used their concept of efficiency for time series analysis. During the summer of 1983, I had an opportunity to visit The Australian National University, and could elucidate the third-order asymptotics of some estimators. I express my sincere thanks to Professor E.J. Hannan for his warmest encouragement and kindness. Multivariate time series analysis seems an important topic. In 1986 I visited Center for Mul tivariate Analysis, University of Pittsburgh. I received a lot of impact from multivariate analysis, and applied many multivariate methods to the higher order asymptotic theory of vector time series. I am very grateful to the late Professor P.R. Krishnaiah for his cooperation and kindness. In Japan my research was mainly performed in Hiroshima University. There is a research group of statisticians who are interested in the asymptotic expansions in statistics. Throughout this book I often used the asymptotic expansion techniques. I thank all the members of this group, especially Professors Y. Fujikoshi and K. Maekawa foItheir helpful discussion. When I was a student of Osaka University I learned multivariate analysis and time series analysis from Professors Masashi Okamoto and T. Nagai, respectively. It is a pleasure to thank them for giving me much of research background.