Springer Series in Statistics

Approximate Distributions of Order Statistics

With Applications to Nonparametric Statistics

Authors: Reiss, Rolf-Dieter

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  • ISBN 978-1-4613-9620-8
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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.

Table of contents (11 chapters)

  • Introduction

    Reiss, R.-D.

    Pages 1-8

  • Distribution Functions, Densities, and Representations

    Reiss, R.-D.

    Pages 11-63

  • Multivariate Order Statistics

    Reiss, R.-D.

    Pages 64-82

  • Inequalities and the Concept of Expansions

    Reiss, R.-D.

    Pages 83-104

  • Approximations to Distributions of Central Order Statistics

    Reiss, R.-D.

    Pages 107-150

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-1-4613-9620-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $139.00
price for USA
  • ISBN 978-1-4613-9622-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Approximate Distributions of Order Statistics
Book Subtitle
With Applications to Nonparametric Statistics
Authors
Series Title
Springer Series in Statistics
Copyright
1989
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York Inc.
eBook ISBN
978-1-4613-9620-8
DOI
10.1007/978-1-4613-9620-8
Softcover ISBN
978-1-4613-9622-2
Series ISSN
0172-7397
Edition Number
1
Number of Pages
XII, 355
Topics