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

  • Masafumi Akahira
  • Kei Takeuchi

Part of the Lecture Notes in Statistics book series (LNS, volume 7)

Table of contents

  1. Front Matter
    Pages I-VII
  2. Masafumi Akahira, Kei Takeuchi
    Pages 1-20
  3. Masafumi Akahira, Kei Takeuchi
    Pages 21-53
  4. Masafumi Akahira, Kei Takeuchi
    Pages 54-80
  5. Masafumi Akahira, Kei Takeuchi
    Pages 81-135
  6. Masafumi Akahira, Kei Takeuchi
    Pages 188-203
  7. Masafumi Akahira, Kei Takeuchi
    Pages 204-230
  8. Back Matter
    Pages 231-247

About this book

Introduction

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.

Keywords

Asymptotische Wirksamkeit Estimator Likelihood Schätzung (Statistik) linear regression

Authors and affiliations

  • Masafumi Akahira
    • 1
  • Kei Takeuchi
    • 2
  1. 1.Department of MathematicsUniversity of Electro-CommunicationsChofu, TokyoJapan
  2. 2.Faculty of EconomicsUniversity of TokyoHongo, Bunkyo-ky, TokyoJapan

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-5927-5
  • Copyright Information Springer-Verlag New York 1981
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-90576-1
  • Online ISBN 978-1-4612-5927-5
  • Series Print ISSN 0930-0325
  • Buy this book on publisher's site
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