On Improved Estimation for Importance Sampling
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.