Asymptotic Efficiency of Statistical Estimators: Concepts and Higher Order Asymptotic Efficiency Concepts and Higher Order Asymptotic Efficiency

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 situat...

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Bibliographic Details
Main Authors: Akahira, Masafumi, Takeuchi, Kei (Author)
Format: eBook
Language:English
Published: New York, NY Springer New York 1981, 1981
Edition:1st ed. 1981
Series:Lecture Notes in Statistics
Subjects:
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Description
Summary: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
Physical Description:242 p online resource
ISBN:9781461259275