On reduction of finite-sample variance by extended Latin hypercube sampling

Abstract

McKay, Conover and Beckman introduced Latin hypercube sampling (LHS) for reducing the variance of Monte Carlo simulations. LHS is a method for stratifying a univariate margin. We consider an extension of LHS to stratify an m-variate margin with orthogonal arrays, after Owen and Tang. We define extended Latin hypercube sampling of strength m (henceforth denoted by ELHS(m)), such that ELHS(1) reduces to LHS. Using the results obtained by Owen, we first derive an explicit formula for the finite-sample variance of ELHS(m). Based on this formula, we give a sufficient condition for variance reduction by ELHS(m), generalizing similar results from McKay et al. for m=1. Actually, our sufficient condition for m=1 contains the sufficient condition of McKay et al. and thus strengthens their result.