The Bootstrap: To Smooth or Not to Smooth,

Abstract

The bootstrap and smoothed bootstrap are considered as alternative methods of estimating properties of unknown distributions such as the sampling error of parameter estimates. Criteria are developed for determining whether it is advantageous to use the smoothed bootstrap rather than the standard bootstrap. Key steps in the argument leading to these criteria include the study of the estimation of linear functionals of distributions and the approximation of general functionals by linear functionals. Consideration of an example, the estimation of the standard error in the variance-stabilized sample correlation coefficient, elucidates previously-published simulation results and also illustrates the use of computer algebraic manipulation as a useful technique in asymptotic statistics. FInally, the various approximations used are vindicated by a simulation study. Keywords: Computer algebra; Density estimation; Kernel; Resampling.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1986
Accession Number
ADA193735

Entities

People

  • B. W. Silverman
  • G. A. Young

Organizations

  • University of Bath

Tags

Communities of Interest

  • C4I
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Accuracy
  • Calculus
  • Coefficients
  • Computers
  • Confidence Limits
  • Data Analysis
  • Data Science
  • Discrete Distribution
  • Distribution Functions
  • Errors
  • Information Science
  • Normal Distribution
  • Probability
  • Probability Density Functions
  • Sampling
  • Simulations
  • Statistics

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Statistical inference.