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Mathematics of Computation

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Asymptotic normality in Monte Carlo integration

Author: Masashi Okamoto
Journal: Math. Comp. 30 (1976), 831-837
MSC: Primary 65C05
MathSciNet review: 0421029
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Abstract: To estimate a multiple integral of a function over the unit cube, Haber proposed two Monte Carlo estimators $ J'_1$ and $ J'_2$ based on 2N and 4N observations, respectively, of the function. He also considered estimators $ D_1^2$ and $ D_2^2$ of the variances of $ J'_1$ and $ J'_2$, respectively. This paper shows that all these estimators are asymptotically normally distributed as N tends to infinity.

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Keywords: Monte Carlo integration, Haber's estimators, asymptotic normality, Lyapunov condition
Article copyright: © Copyright 1976 American Mathematical Society

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