Abstract
SUMMARY: We introduce an empirical method of importance resampling, which does not require analytical calculation of the resampling probabilities. Our method can easily be used as part of a general algorithm for Monte Carlo calculation of bootstrap confidence intervals and hypothesis tests. It produces consistent, efficient and unbiased Monte Carlo approximations. We also present a very general but elementary account of importance resampling, which shows that even optimal importance resampling cannot improve on uniform resampling for calculating bootstrap estimates of bias, variance, skewness and related quantities. This result demonstrates a major difference between importance resampling and other approaches to efficient bootstrap simulation, such as balanced resampling and antithetic resampling, which produce significant improvements in efficiency for a wide range of problems involving the bootstrap.
Original language | English (US) |
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Pages (from-to) | 161-167 |
Number of pages | 7 |
Journal | Biometrika |
Volume | 78 |
Issue number | 1 |
DOIs | |
State | Published - Mar 1991 |
Externally published | Yes |
Keywords
- Bootstrap
- Confidence interval
- Distribution function
- Efficiency
- Importance sampling
- Monte Carlo
- Quantile
- Simulation
- Uniform resampling
ASJC Scopus subject areas
- Statistics and Probability
- General Mathematics
- Agricultural and Biological Sciences (miscellaneous)
- General Agricultural and Biological Sciences
- Statistics, Probability and Uncertainty
- Applied Mathematics