Ab. Owen, A CENTRAL-LIMIT-THEOREM FOR LATIN HYPERCUBE SAMPLING, Journal of the Royal Statistical Society. Series B: Methodological, 54(2), 1992, pp. 541-551
Citations number
17
Journal title
Journal of the Royal Statistical Society. Series B: Methodological
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.