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Approximate Distributions of Order Statistics

With Applications to Nonparametric Statistics

  • Book
  • © 1989

Overview

Authors:
  1. R.-D. Reiss

    1. Fachbereich 6, Mathematik, Universität Gesamthochschule Siegen, Siegen, Federal Republic of Germany

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

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xii
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  2. Introduction

    1. Introduction

      • R.-D. Reiss
      Pages 1-8

  3. Exact Distributions and Basic Tools

    1. Front Matter

      Pages 9-9
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    2. Distribution Functions, Densities, and Representations

      • R.-D. Reiss
      Pages 11-63

    3. Multivariate Order Statistics

      • R.-D. Reiss
      Pages 64-82

    4. Inequalities and the Concept of Expansions

      • R.-D. Reiss
      Pages 83-104

  4. Asymptotic Theory

    1. Front Matter

      Pages 105-105
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    2. Approximations to Distributions of Central Order Statistics

      • R.-D. Reiss
      Pages 107-150

    3. Approximations to Distributions of Extremes

      • R.-D. Reiss
      Pages 151-205

    4. Other Important Approximations

      • R.-D. Reiss
      Pages 206-228

    5. Approximations in the Multivariate Case

      • R.-D. Reiss
      Pages 229-239

  5. Statistical Models and Procedures

    1. Front Matter

      Pages 241-241
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    2. Evaluating the Quantile and Density Quantile Function

      • R.-D. Reiss
      Pages 243-271

    3. Extreme Value Models

      • R.-D. Reiss
      Pages 272-291

    4. Approximate Sufficiency of Sparse Order Statistics

      • R.-D. Reiss
      Pages 292-317

  6. Back Matter

    Pages 318-355
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Keywords

About this book

This book is designed as a unified and mathematically rigorous treatment of some recent developments of the asymptotic distribution theory of order statistics (including the extreme order statistics) that are relevant for statistical theory and its applications. Particular emphasis is placed on results concern­ ing the accuracy oflimit theorems, on higher order approximations, and other approximations in quite a general sense. Contrary to the classical limit theorems that primarily concern the weak convergence of distribution functions, our main results will be formulated in terms of the variational and the Hellinger distance. These results will form the proper springboard for the investigation of parametric approximations of nonparametric models of joint distributions of order statistics. The approxi­ mating models include normal as well as extreme value models. Several applications will show the usefulness of this approach. Other recent developments in statistics like nonparametric curve estima­ tion and the bootstrap method will be studied as far as order statistics are concerned. 1n connection with this, graphical methods will, to some extent, be explored.

Authors and Affiliations

  • Fachbereich 6, Mathematik, Universität Gesamthochschule Siegen, Siegen, Federal Republic of Germany

    R.-D. Reiss

Bibliographic Information

  • Book Title: Approximate Distributions of Order Statistics

  • Book Subtitle: With Applications to Nonparametric Statistics

  • Authors: R.-D. Reiss

  • Series Title: Springer Series in Statistics

  • DOI: https://doi.org/10.1007/978-1-4613-9620-8

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York Inc. 1989

  • Softcover ISBN: 978-1-4613-9622-2Published: 21 December 2011

  • eBook ISBN: 978-1-4613-9620-8Published: 06 December 2012

  • Series ISSN: 0172-7397

  • Series E-ISSN: 2197-568X

  • Edition Number: 1

  • Number of Pages: XII, 355

  • Topics: Applications of Mathematics

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