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Asymptotic Expansions for General Statistical Models

  • Johann Pfanzagl

Part of the Lecture Notes in Statistics book series (LNS, volume 31)

Table of contents

  1. Front Matter
    Pages N2-VII
  2. Johann Pfanzagl
    Pages 1-17
  3. Johann Pfanzagl
    Pages 18-56
  4. Johann Pfanzagl
    Pages 86-104
  5. Johann Pfanzagl
    Pages 105-127
  6. Johann Pfanzagl
    Pages 128-152
  7. Johann Pfanzagl
    Pages 153-197
  8. Johann Pfanzagl
    Pages 198-244
  9. Johann Pfanzagl
    Pages 333-381
  10. Johann Pfanzagl
    Pages 382-427
  11. Johann Pfanzagl
    Pages 428-450
  12. Johann Pfanzagl
    Pages 451-486
  13. Back Matter
    Pages 487-509

About this book

Introduction

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.

Keywords

approximation behavior construction distribution estimator function functional functions Mathematica probability statistical theory statistics Volume

Authors and affiliations

  • Johann Pfanzagl
    • 1
  1. 1.Mathematisches InstitutUniversität zu KölnKöln 41Federal Republic of Germany

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4615-6479-9
  • Copyright Information Springer-Verlag New York 1985
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-96221-4
  • Online ISBN 978-1-4615-6479-9
  • Series Print ISSN 0930-0325
  • Series Online ISSN 2197-7186
  • Buy this book on publisher's site