On improved estimation for importance sampling
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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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|
|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|Status:||Not Peer Reviewed|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|
|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.|
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