Sums, trimmed sums and extremes
Author(s)
Bibliographic Information
Sums, trimmed sums and extremes
(Progress in probability / series editors, Thomas Liggett, Charles Newman, Loren Pitt, v. 23)
Birkhäuser, 1991
- : us
- : sz
Available at 23 libraries
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
  Nagano
  Gifu
  Shizuoka
  Aichi
  Mie
  Shiga
  Kyoto
  Osaka
  Hyogo
  Nara
  Wakayama
  Tottori
  Shimane
  Okayama
  Hiroshima
  Yamaguchi
  Tokushima
  Kagawa
  Ehime
  Kochi
  Fukuoka
  Saga
  Nagasaki
  Kumamoto
  Oita
  Miyazaki
  Kagoshima
  Okinawa
  Korea
  China
  Thailand
  United Kingdom
  Germany
  Switzerland
  France
  Belgium
  Netherlands
  Sweden
  Norway
  United States of America
Note
Includes bibliographical references
Description and Table of Contents
Description
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.
Table of Contents
I Approaches to Trimming and Self-normalization Based on Analytic Methods.- Asymptotic Behavior of Partial Sums: A More Robust Approach Via Trimming and Self-Normalization.- Weak Convergence of Trimmed Sums.- Invariance Principles and Self-Normalizations for Sums Trimmed According to Choice of Influence Function.- On Joint Estimation of an Exponent of Regular Variation and an Asymmetry Parameter for Tail Distributions.- Center, Scale and Asymptotic Normality for Censored Sums of Independent, Nonidentically Distributed Random Variables.- A Review of Some Asymptotic Properties of Trimmed Sums of Multivariate Data.- II The Quantile-Transform-Empirical-Process Approach to Trimming.- The Quantile-Transform-Empirical-Process Approach to Limit Theorems for Sums of Order Statistics.- A Note on Weighted Approximations to the Uniform Empirical and Quantile Processes.- Limit Theorems for the Petersburg Game.- A Probabilistic Approach to the Tails of Infinitely Divisible Laws.- The Quantile-Transform Approach to the Asymptotic Distribution of Modulus Trimmed Sums.- On the Asymptotic Behavior of Sums of Order Statistics from a Distribution with a Slowly Varying Upper Tail.- Limit Results for Linear Combinations.- Non-Normality of a Class of Random Variables.
by "Nielsen BookData"