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.
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