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Asymptotic Efficiency Of Statistical Estimators Concepts And Higher Order Asymptotic Efficiency


Asymptotic Efficiency Of Statistical Estimators Concepts And Higher Order Asymptotic Efficiency
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Asymptotic Efficiency Of Statistical Estimators Concepts And Higher Order Asymptotic Efficiency


Asymptotic Efficiency Of Statistical Estimators Concepts And Higher Order Asymptotic Efficiency
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Author : Masafumi Akahira
language : en
Publisher: Springer
Release Date : 2011-11-22

Asymptotic Efficiency Of Statistical Estimators Concepts And Higher Order Asymptotic Efficiency 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 2011-11-22 with Mathematics categories.


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.



Asymptotic Efficiency Of Statistical Estimators Concepts And Higher Order Asymptotic Efficiency


Asymptotic Efficiency Of Statistical Estimators Concepts And Higher Order Asymptotic Efficiency
DOWNLOAD
Author : Masafumi Akahira
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Asymptotic Efficiency Of Statistical Estimators Concepts And Higher Order Asymptotic Efficiency 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.


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.



Joint Statistical Papers Of Akahira And Takeuchi


Joint Statistical Papers Of Akahira And Takeuchi
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Author : Masafumi Akahira
language : en
Publisher: World Scientific
Release Date : 2003-08-13

Joint Statistical Papers Of Akahira And Takeuchi written by Masafumi Akahira and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-08-13 with Mathematics categories.


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.



Probability Theory And Mathematical Statistics


Probability Theory And Mathematical Statistics
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Author : Shinzo Watanabe
language : en
Publisher: Springer
Release Date : 2006-11-15

Probability Theory And Mathematical Statistics written by Shinzo Watanabe and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.


These proceedings of the fifth joint meeting of Japanese and Soviet probabilists are a sequel to Lecture Notes in Mathematics Vols. 33O, 550 and 1O21. They comprise 61 original research papers on topics including limit theorems, stochastic analysis, control theory, statistics, probabilistic methods in number theory and mathematical physics.



Statistical Estimation For Truncated Exponential Families


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.



Probability Theory And Mathematical Statistics


Probability Theory And Mathematical Statistics
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Author : K. Ito
language : en
Publisher: Springer
Release Date : 2006-11-15

Probability Theory And Mathematical Statistics written by K. Ito and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.




Selected Papers On Probability And Statistics


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.



Contemporary Developments In Statistical Theory


Contemporary Developments In Statistical Theory
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Author : Soumendra Lahiri
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-02

Contemporary Developments In Statistical Theory written by Soumendra Lahiri 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 2013-12-02 with Mathematics categories.


This volume highlights Prof. Hira Koul’s achievements in many areas of Statistics, including Asymptotic theory of statistical inference, Robustness, Weighted empirical processes and their applications, Survival Analysis, Nonlinear time series and Econometrics, among others. Chapters are all original papers that explore the frontiers of these areas and will assist researchers and graduate students working in Statistics, Econometrics and related areas. Prof. Hira Koul was the first Ph.D. student of Prof. Peter Bickel. His distinguished career in Statistics includes the receipt of many prestigious awards, including the Senior Humbolt award (1995), and dedicated service to the profession through editorial work for journals and through leadership roles in professional societies, notably as the past president of the International Indian Statistical Association. Prof. Hira Koul has graduated close to 30 Ph.D. students, and made several seminal contributions in about 125 innovative research papers. The long list of his distinguished collaborators is represented by the contributors to this volume.



Asymptotic Theory Of Statistical Inference For Time Series


Asymptotic Theory Of Statistical Inference For Time Series
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Author : Masanobu Taniguchi
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Asymptotic Theory Of Statistical Inference For Time Series 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.


There has been much demand for the statistical analysis of dependent ob servations in many fields, for example, economics, engineering and the nat ural sciences. A model that describes the probability structure of a se ries of dependent observations is called a stochastic process. 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 autoregressive (AR), moving average (MA), and autoregressive moving average (ARMA) processes. We deal with a wide variety of stochastic processes, for example, non-Gaussian linear processes, long-memory processes, nonlinear processes, orthogonal increment process es, and continuous time processes. For them we develop not only the usual estimation and testing theory but also many other statistical methods and techniques, such as discriminant analysis, cluster analysis, nonparametric methods, higher order asymptotic theory in view of differential geometry, large deviation principle, and saddlepoint approximation. Because it is d ifficult to use the exact distribution theory, the discussion is based on the asymptotic theory. Optimality of various procedures is often shown by use of local asymptotic normality (LAN), which is due to LeCam. This book is suitable as a professional reference book on statistical anal ysis of stochastic processes or as a textbook for students who specialize in statistics. It will also be useful to researchers, including those in econo metrics, mathematics, and seismology, who utilize statistical methods for stochastic processes.



A Celebration Of Statistics


A Celebration Of Statistics
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Author : Anthony C. Atkinson
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

A Celebration Of Statistics written by Anthony C. Atkinson 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 International Statistical Institute was founded in 1885 and is therefore one of the world's oldest international scientific societies. The field of statistics is still expanding rapidly and possesses a rich variety of applications in many areas of human activity such as science, government, business, industry, and everyday affairs. In consequence, the celebration of the Institute's centenary in 1985 is of considerable interest not only to statisticians but also more widely to the international scientific community. As part of its centennial celebration planning the Institute decided to publish a volume of papers representing the immensely wide range of interests encompassed by statistics in its international context, viewed both from a historical and from a contemporary standpoint. We were fortunate in securing the services of Anthony Atkinson and Stephen Fienberg as Editors of this volume: they have worked hard over a period of several years to put together a most fascinating collection of papers. On behalf of the Institute it is my pleasant duty to thank them and the authors for their contributions. J. DURBIN, President International Statistical Institute Preface The papers in this volume were prepared to help celebrate the centenary of the International Statistical Institute. During the lSI's first 100 years statistics has matured, both as a scientific discipline and as a profession, in ways that the lSI's founders could not possibly have imagined.