### 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 language | English (US) |
---|---|

Pages (from-to) | 451-460 |

Number of pages | 10 |

Journal | Computational Statistics and Data Analysis |

Volume | 15 |

Issue number | 4 |

DOIs | |

State | Published - 1993 |

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### 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.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Almost-exact parametric bootstrap calculation via the saddlepoint approximation

AU - Rocke, David M

PY - 1993

Y1 - 1993

N2 - 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.

AB - 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.

KW - Gaussian quadrature

KW - Maximum likelihood

KW - Numerical integration

KW - Reliability

KW - Stress-strength problems

UR - http://www.scopus.com/inward/record.url?scp=43949169312&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=43949169312&partnerID=8YFLogxK

U2 - 10.1016/0167-9473(93)90176-T

DO - 10.1016/0167-9473(93)90176-T

M3 - Article

AN - SCOPUS:43949169312

VL - 15

SP - 451

EP - 460

JO - Computational Statistics and Data Analysis

JF - Computational Statistics and Data Analysis

SN - 0167-9473

IS - 4

ER -