Almost-exact parametric bootstrap calculation via the saddlepoint approximation

Research output: Contribution to journalArticle

Abstract

One impediment to wider use of bootstrap methods is the large amount of computer time often required to compute bootstrap estimates. This paper shows how the saddlepoint approximation method can be used in certain situations to give very accurate parametric bootstrap statistics with a much smaller amount of calculation. Essentially, the problem of computing an n-dimentional integral (where n is the sample size) by Monte Carlo is reduced to an integral whose dimension is that of the parameter space, which is usually much smaller. This allows accurate numerical integration techniques to be used in place of simulation. The method should be especially effective for maximum likelihood in linear exponential family problems; it is illustrated by application to a problem in reliability.

Original languageEnglish (US)
Pages (from-to)451-460
Number of pages10
JournalComputational Statistics and Data Analysis
Volume15
Issue number4
DOIs
StatePublished - 1993

Fingerprint

Parametric Bootstrap
Saddlepoint Approximation
Maximum likelihood
Statistics
Saddle Point Method
Bootstrap Method
Exponential Family
Approximation Methods
Bootstrap
Numerical integration
Maximum Likelihood
Parameter Space
Sample Size
Computing
Estimate
Parametric bootstrap
Integral
Saddlepoint
Approximation
Simulation

Keywords

  • Gaussian quadrature
  • Maximum likelihood
  • Numerical integration
  • Reliability
  • Stress-strength problems

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Statistics, Probability and Uncertainty
  • Electrical and Electronic Engineering
  • Computational Mathematics
  • Numerical Analysis
  • Statistics and Probability

Cite this

Almost-exact parametric bootstrap calculation via the saddlepoint approximation. / Rocke, David M.

In: Computational Statistics and Data Analysis, Vol. 15, No. 4, 1993, p. 451-460.

Research output: Contribution to journalArticle

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