A general theory for orthogonal array based Latin hypercube sampling

Orthogonal array based Latin hypercube sampling (LHS) is popularly adopted for computer experiments. Because of its stratification on multivariate margins in addition to univariate uniformity, the associated samples may provide better estimators for the gross mean of a complex function on a domain. In this paper, for some LHS methods based on an orthogonal array of strength t, a unified expression of the variance of the sample mean is developed by introducing a new discrete function. An approximate estimator for the variance of the sample mean is also established that is helpful in obtaining the confidence interval of the gross mean. We extend these statistical properties to three types of LHS: strong orthogonal array-based LHS, nested orthogonal array-based LHS, and correlation-controlled orthogonal array-based LHS. Some simulations are given to verify our results.