A CENTRAL-LIMIT-THEOREM FOR LATIN HYPERCUBE SAMPLING

Latin hypercube sampling (LHS) is a technique for Monte Carlo integrat ion, due to McKay, Conover and Beckman. M. Stein proved that LHS integ rals have smaller variance than independent and identically distribute d Monte Carlo integration, the extent of the variance reduction depend ing on the extent to which the integrand is additive. We extend Stein' s work to prove a central limit theorem. Variance estimation methods f or 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. W e also show how to combine control variates with LHS. Finally we show how these results lead to a frequentist approach to computer experimen tation.