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Sums, Trimmed Sums and Extremes

  • Book
  • © 1991

Overview

Editors:
  1. Marjorie G. Hahn

    1. Department of Mathematics, Tufts University, Medford, USA

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    You can also search for this editor in PubMed   Google Scholar

  2. David M. Mason

    1. Department of Mathematical Sciences, University of Delware, Newark, USA

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    You can also search for this editor in PubMed   Google Scholar

  3. Daniel C. Weiner

    1. Department of Mathematics, Boston University, Boston, USA

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Progress in Probability (PRPR, volume 23)

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Table of contents (14 chapters)

  1. Front Matter

    Pages i-viii
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  2. Approaches to Trimming and Self-normalization Based on Analytic Methods

    1. Front Matter

      Pages ix-ix
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    2. Asymptotic Behavior of Partial Sums: A More Robust Approach Via Trimming and Self-Normalization

      • Marjorie G. Hahn, Jim Kuelbs, Daniel C. Weiner
      Pages 1-53

    3. Weak Convergence of Trimmed Sums

      • Philip S. Griffin, William E. Pruitt
      Pages 55-80

    4. Invariance Principles and Self-Normalizations for Sums Trimmed According to Choice of Influence Function

      • Hamid Ould-Rouis
      Pages 81-110

    5. On Joint Estimation of an Exponent of Regular Variation and an Asymmetry Parameter for Tail Distributions

      • Marjorie G. Hahn, Daniel C. Weiner
      Pages 111-134

    6. Center, Scale and Asymptotic Normality for Censored Sums of Independent, Nonidentically Distributed Random Variables

      • Daniel Charles Weiner
      Pages 135-177

    7. A Review of Some Asymptotic Properties of Trimmed Sums of Multivariate Data

      • R. A. Maller
      Pages 179-211

  3. The Quantile-Transform-Empirical-Process Approach to Trimming

    1. Front Matter

      Pages 215-215
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    2. The Quantile-Transform-Empirical-Process Approach to Limit Theorems for Sums of Order Statistics

      • Sándor Csörgő, Erich Haeusler, David M. Mason
      Pages 215-267

    3. A Note on Weighted Approximations to the Uniform Empirical and Quantile Processes

      • David M. Mason
      Pages 269-283

    4. Limit Theorems for the Petersburg Game

      • Sándor Csörgő, Rossitza Dodunekova
      Pages 285-315

    5. A Probabilistic Approach to the Tails of Infinitely Divisible Laws

      • Sándor Csörgő, David M. Mason
      Pages 317-335

    6. The Quantile-Transform Approach to the Asymptotic Distribution of Modulus Trimmed Sums

      • Sándor Csörgő, Erich Haeusler, David M. Mason
      Pages 337-353

    7. On the Asymptotic Behavior of Sums of Order Statistics from a Distribution with a Slowly Varying Upper Tail

      • Erich Haeusler, David M. Mason
      Pages 355-376

    8. Limit Results for Linear Combinations

      • Galen R. Shorack
      Pages 377-391

    9. Non-Normality of a Class of Random Variables

      • David M. Mason, Galen R. Shorack
      Pages 393-416

  4. Back Matter

    Pages 417-417
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Keywords

About this book

The past decade has seen a resurgence of interest in the study of the asymp­ totic behavior of sums formed from an independent sequence of random variables. In particular, recent attention has focused on the interaction of the extreme summands with, and their influence upon, the sum. As ob­ served by many authors, the limit theory for sums can be meaningfully expanded far beyond the scope of the classical theory if an "intermediate" portion (i. e. , an unbounded number but a vanishingly small proportion) of the extreme summands in the sum are deleted or otherwise modified (''trimmed',). The role of the normal law is magnified in these intermediate trimmed theories in that most or all of the resulting limit laws involve variance-mixtures of normals. The objective of this volume is to present the main approaches to this study of intermediate trimmed sums which have been developed so far, and to illustrate the methods with a variety of new results. The presentation has been divided into two parts. Part I explores the approaches which have evolved from classical analytical techniques (condi­ tionin~, Fourier methods, symmetrization, triangular array theory). Part II is Msed on the quantile transform technique and utilizes weak and strong approximations to uniform empirical process. The analytic approaches of Part I are represented by five articles involving two groups of authors.

Editors and Affiliations

  • Department of Mathematics, Tufts University, Medford, USA

    Marjorie G. Hahn

  • Department of Mathematical Sciences, University of Delware, Newark, USA

    David M. Mason

  • Department of Mathematics, Boston University, Boston, USA

    Daniel C. Weiner

Bibliographic Information

  • Book Title: Sums, Trimmed Sums and Extremes

  • Editors: Marjorie G. Hahn, David M. Mason, Daniel C. Weiner

  • Series Title: Progress in Probability

  • DOI: https://doi.org/10.1007/978-1-4684-6793-2

  • Publisher: Birkhäuser Boston, MA

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkhäuser Boston 1991

  • Softcover ISBN: 978-1-4684-6795-6Published: 18 April 2012

  • eBook ISBN: 978-1-4684-6793-2Published: 06 December 2012

  • Series ISSN: 1050-6977

  • Series E-ISSN: 2297-0428

  • Edition Number: 1

  • Number of Pages: X, 418

  • Topics: Sequences, Series, Summability, Probability Theory and Stochastic Processes

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