Estimation in Semiparametric Models

Some Recent Developments

  • Johann Pfanzagl

Part of the Lecture Notes in Statistics book series (LNS, volume 63)

Table of contents

  1. Front Matter
    Pages i-iii
  2. Introduction

    1. Johann Pfanzagl
      Pages 1-1
  3. Survey of basic theory

    1. Johann Pfanzagl
      Pages 2-3
    2. Johann Pfanzagl
      Pages 7-16
    3. Johann Pfanzagl
      Pages 17-22
    4. Johann Pfanzagl
      Pages 23-34
    5. Johann Pfanzagl
      Pages 35-37
  4. Semiparametric families admitting a sufficient statistic

    1. Johann Pfanzagl
      Pages 38-47
    2. Johann Pfanzagl
      Pages 48-52
    3. Johann Pfanzagl
      Pages 53-87
  5. Auxiliary results

    1. Johann Pfanzagl
      Pages 88-105
  6. Back Matter
    Pages 106-112

About this book

Introduction

Assume one has to estimate the mean J x P( dx) (or the median of P, or any other functional t;;(P)) on the basis ofi.i.d. observations from P. Ifnothing is known about P, then the sample mean is certainly the best estimator one can think of. If P is known to be the member of a certain parametric family, say {Po: {) E e}, one can usually do better by estimating {) first, say by {)(n)(.~.), and using J XPo(n)(;r.) (dx) as an estimate for J xPo(dx). There is an "intermediate" range, where we know something about the unknown probability measure P, but less than parametric theory takes for granted. Practical problems have always led statisticians to invent estimators for such intermediate models, but it usually remained open whether these estimators are nearly optimal or not. There was one exception: The case of "adaptivity", where a "nonparametric" estimate exists which is asymptotically optimal for any parametric submodel. The standard (and for a long time only) example of such a fortunate situation was the estimation of the center of symmetry for a distribution of unknown shape.

Keywords

DEX boundary element method development distribution eXist estimator function functional measure median probability probability measure symmetry time

Authors and affiliations

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

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-3396-1
  • Copyright Information Springer-Verlag New York 1990
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-97238-1
  • Online ISBN 978-1-4612-3396-1
  • Series Print ISSN 0930-0325
  • About this book