Variance Reduction Methods II 2 1 . 1 The Importance Sampling Estimator

For this problem, however, the usual approach would be completely inadequate since approximating θ to any reasonable degree of accuracy would require n to be inordinately large. For example, on average we would have to set n ≈ 2.7014× 10 in order to obtain just one non-zero value of I. Clearly this is impractical and a much smaller value of n would have to be used. Using a much smaller value of n, however, would almost inevitably result in an estimate, θ̂n = 0, and an approximate confidence interval [L,U ] = [0, 0]! So the naive approach does not work. We could try to use the variance reduction techniques we have seen in the course so far, but they would provide little, if any, help.