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A Central Limit Theorem for Latin Hypercube Sampling
Art B. Owen
Journal of the Royal Statistical Society. Series B (Methodological)
Vol. 54, No. 2 (1992), pp. 541-551
Stable URL: http://www.jstor.org/stable/2346140
Page Count: 11
You can always find the topics here!Topics: Statistical variance, Estimation methods, Additivity, Estimate reliability, Statism, Central limit theorem, Confidence interval, Data smoothing, Skewed distribution, Random variables
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Latin hypercube sampling (LHS) is a technique for Monte Carlo integration, due to McKay, Conover and Beckman. M. Stein proved that LHS integrals have smaller variance than independent and identically distributed Monte Carlo integration, the extent of the variance reduction depending on the extent to which the integrand is additive. We extend Stein's work to prove a central limit theorem. Variance estimation methods for nonparametric regression can be adapted to provide N1/2-consistent estimates of the asymptotic variance in LHS. Moreover the skewness can be estimated at this rate. The variance reduction may be explained in terms of certain control variates that cannot be directly measured. We also show how to combine control variates with LHS. Finally we show how these results lead to a frequentist approach to computer experimentation.
Journal of the Royal Statistical Society. Series B (Methodological) © 1992 Royal Statistical Society