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Robust Asymptotic Statistics

Volume I

  • Book
  • © 1994

Overview

Authors:
  1. Helmut Rieder

    1. Lehrstühl VII für Mathematik, Universität Bayreuth, Bayreuth, Germany

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  • This volume gives a rigorous account of the asymptotic theory of robust statistics, from the viewpoint of optimally robust functionals and their unbiased estimators and tests.

Part of the book series: Springer Series in Statistics (SSS)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xxii
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  2. Von Mises Functionals

    • Helmut Rieder
    Pages 1-37

  3. Log Likelihoods

    • Helmut Rieder
    Pages 39-70

  4. Asymptotic Statistics

    • Helmut Rieder
    Pages 71-122

  5. Nonparametric Statistics

    • Helmut Rieder
    Pages 123-164

  6. Optimal Influence Curves

    • Helmut Rieder
    Pages 165-218

  7. Stable Constructions

    • Helmut Rieder
    Pages 219-260

  8. Robust Regression

    • Helmut Rieder
    Pages 261-330

  9. Back Matter

    Pages 331-391
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Keywords

About this book

1 To the king, my lord, from your servant Balasi : 2 ... The king should have a look. Maybe the scribe who reads to the king did not understand . . . . shall I personally show, with this tablet that I am sending to the king, my lord, how the omen was written. 3 Really, he who has not followed the text with his finger cannot possibly understand it. This book is about optimally robust functionals and their unbiased esti­ mators and tests. Functionals extend the parameter of the assumed ideal center model to neighborhoods of this model that contain the actual distri­ bution. The two principal questions are (F): Which functional to choose? and (P): Which statistical procedure to use for the selected functional? Using a local asymptotic framework, we deal with both problems by linking up nonparametric statistical optimality with infinitesimal robust­ ness criteria. Thus, seemingly separate developments in robust statistics are presented in a unifying way.

Authors and Affiliations

  • Lehrstühl VII für Mathematik, Universität Bayreuth, Bayreuth, Germany

    Helmut Rieder

Bibliographic Information

  • Book Title: Robust Asymptotic Statistics

  • Book Subtitle: Volume I

  • Authors: Helmut Rieder

  • Series Title: Springer Series in Statistics

  • DOI: https://doi.org/10.1007/978-1-4684-0624-5

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York, Inc. 1994

  • Softcover ISBN: 978-1-4684-0626-9Published: 16 February 2012

  • eBook ISBN: 978-1-4684-0624-5Published: 06 December 2012

  • Series ISSN: 0172-7397

  • Series E-ISSN: 2197-568X

  • Edition Number: 1

  • Number of Pages: XXII, 390

  • Topics: Probability Theory and Stochastic Processes

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