Bootstrapping the Sample Mean for Data with Infinite Variance

Abstract

When data comes from a distribution belonging to the domain of attraction of a stable law, Athreya (1987a) showed that the bootstrapped sample mean has random limiting distribution, implying that the naive bootstrap could fail in the heavy-tailed case. The goal here is to classify all possible limiting distributions of the bootstrapped sample mean when the sample comes from a distribution with infinite variance, allowing the broadest possible setting for the (nonrandom) scaling, the resample size, and the mode of convergence (in law). The limiting distributions turn out to be infinitely divisible with possibly random Levy measure, depending on the resample size. An averaged-bootstrap algorithm is then introduced which eliminates any randomness in the limiting distribution. Finally, it is shown that (on the average) the limiting distribution in the domain of (partial) attraction of a stable law.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1990
Accession Number
ADA225870

Entities

People

  • Edward Carlstein
  • Stamatis Cambanis
  • Wei Wu

Organizations

  • University of North Carolina at Chapel Hill

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Classification
  • Convergence
  • Data Science
  • Demography
  • Distribution Functions
  • Information Science
  • New York
  • Normal Distribution
  • North Carolina
  • Probability
  • Random Variables
  • Security
  • Standardization
  • Statistics
  • Stochastic Processes
  • Universities

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.
  • Regression Analysis.