Asymptotic normality in Monte Carlo integration

Abstract

To estimate a multiple integral of a function over the unit cube, Haber proposed two Monte Carlo estimators J 1 ′ J’_1 and J 2 ′ J’_2 based on 2N and 4N observations, respectively, of the function. He also considered estimators D 1 2 D_1^2 and D 2 2 D_2^2 of the variances of J 1 ′ J’_1 and J 2 ′ J’_2 , respectively. This paper shows that all these estimators are asymptotically normally distributed as N tends to infinity.