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Estimation in Semiparametric Models

Some Recent Developments

  • Book
  • © 1990

Overview

Authors:
  1. Johann Pfanzagl

    1. Mathematisches Institut, Universität zu Köln, Köln 41, Federal Republic of Germany

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

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-iii
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  2. Introduction

    1. Introduction

      • Johann Pfanzagl
      Pages 1-1

  3. Survey of basic theory

    1. Tangent spaces and gradients

      • Johann Pfanzagl
      Pages 2-3

    2. Asymptotic bounds for the concentration of estimator-sequences

      • Johann Pfanzagl
      Pages 4-6

    3. Constructing estimator-sequences

      • Johann Pfanzagl
      Pages 7-16

    4. Estimation in semiparametric models

      • Johann Pfanzagl
      Pages 17-22

    5. Families of gradients

      • Johann Pfanzagl
      Pages 23-34

    6. Estimating equations

      • Johann Pfanzagl
      Pages 35-37

  4. Semiparametric families admitting a sufficient statistic

    1. A special semiparametric model

      • Johann Pfanzagl
      Pages 38-47

    2. Mixture models

      • Johann Pfanzagl
      Pages 48-52

    3. Examples of mixture models

      • Johann Pfanzagl
      Pages 53-87

  5. Auxiliary results

    1. Auxiliary results

      • Johann Pfanzagl
      Pages 88-105

  6. Back Matter

    Pages 106-112
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Keywords

About this book

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.

Authors and Affiliations

  • Mathematisches Institut, Universität zu Köln, Köln 41, Federal Republic of Germany

    Johann Pfanzagl

Bibliographic Information

  • Book Title: Estimation in Semiparametric Models

  • Book Subtitle: Some Recent Developments

  • Authors: Johann Pfanzagl

  • Series Title: Lecture Notes in Statistics

  • DOI: https://doi.org/10.1007/978-1-4612-3396-1

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1990

  • Softcover ISBN: 978-0-387-97238-1Published: 06 April 1990

  • eBook ISBN: 978-1-4612-3396-1Published: 06 December 2012

  • Series ISSN: 0930-0325

  • Series E-ISSN: 2197-7186

  • Edition Number: 1

  • Number of Pages: III, 112

  • Topics: Applications of Mathematics

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