Brazilian Journal of Probability and Statistics

On improved estimation for importance sampling

David Firth

Full-text: Open access

Abstract

The standard estimator used in conjunction with importance sampling in Monte Carlo integration is unbiased but inefficient. An alternative estimator is discussed, based on the idea of a difference estimator, which is asymptotically optimal. The improved estimator uses the importance weight as a control variate, as previously studied by Hesterberg (Ph.D. Dissertation, Stanford University (1988); Technometrics 37 (1995) 185–194; Statistics and Computing 6 (1996) 147–157); it is routinely available and can deliver substantial additional variance reduction. Finite-sample performance is illustrated in a sequential testing example. Connections are made with methods from the survey-sampling literature.

Article information

Source
Braz. J. Probab. Stat. Volume 25, Number 3 (2011), 437-443.

Dates
First available in Project Euclid: 22 August 2011

Permanent link to this document
https://projecteuclid.org/euclid.bjps/1313973403

Digital Object Identifier
doi:10.1214/11-BJPS155

Mathematical Reviews number (MathSciNet)
MR2832895

Zentralblatt MATH identifier
1282.65014

Keywords
Difference estimator Horvitz–Thompson estimator regression estimator simulation variance reduction

Citation

Firth, David. On improved estimation for importance sampling. Braz. J. Probab. Stat. 25 (2011), no. 3, 437--443. doi:10.1214/11-BJPS155. https://projecteuclid.org/euclid.bjps/1313973403


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References

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