Firth, David (2011) On improved estimation for importance sampling. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology. (Working papers, Vol.2011).

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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 (1988 PhD Dissertation, Stanford University; 1995, Technometrics; 1996, Statistics and Computing); 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.

Item Type:	Working or Discussion Paper (Working Paper)
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH):	Monte Carlo method, Estimation theory, Analysis of variance
Series Name:	Working papers
Publisher:	University of Warwick. Centre for Research in Statistical Methodology
Place of Publication:	Coventry
Date:	2011
Volume:	Vol.2011
Number:	No.14
Number of Pages:	7
Status:	Not Peer Reviewed
Access rights to Published version:	Open Access
Funder:	Engineering and Physical Sciences Research Council (EPSRC)
Version or Related Resource:	Firth, D. (2011). On improved estimation for importance sampling. Brazilian Journal of Probability and Statistics, 25(3), pp. 437-443. http://wrap.warwick.ac.uk/id/eprint/41191
Related URLs:	Related item in WRAP
References:	Evans, M. and Swartz, T. B. (2000). Approximating Integrals via Monte Carlo and Deterministic Methods. Oxford: Oxford University Press. Firth, D. and Bennett, K. E. (1998). Robust models in probability sampling (with discussion). Journal of the Royal Statistical Society B 60 3–21. Hammersley, J. M. and Handscomb, D. C. (1964). Monte Carlo Methods. London: Chapman and Hall. Hesterberg, T. C. (1988). Advances in Importance Sampling. PhD thesis, Stanford University. Hesterberg, T. C. (1995).Weighted average importance sampling and defensive mixture distributions. Technometrics 37 185–194. Hesterberg, T. C. (1996). Control variates and importance sampling for efficient bootstrap simulations. Statistics and Computing 6 147–157. Ripley, B. D. (1987). Stochastic Simulation. New York: Wiley. Robert, C. P. and Casella, G. (2005). Monte Carlo Statistical Methods (2nd ed). New York: Springer. S¨arndal, C. E., Swensson, B. and Wretman, J. H. (1992). Model Assisted Survey Sampling. New York: Springer. Siegmund, D. (1976). Importance sampling in the Monte Carlo study of sequential tests. Annals of Statistics 25 673–684. Van Deusen, P. C. (1995). Difference sampling as an alternative to importance sampling. Canadian Journal of Forest Research 25 487–490.
URI:	http://wrap.warwick.ac.uk/id/eprint/35060

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