On Latin hypercube sampling

This paper contains a collection of results on Latin hypercube sampling. The first result is a Berry-Esseen-type bound for the multivariate central limit theorem of the sample mean $\hat{\mu}_n$ based on a Latin hypercube sample. The second establishes sufficient conditions on the convergence rate in the strong law for $\hat{\mu}_n$. Finally motivated by the concept of empirical likelihood, a way of constructing nonparametric confidence regions based on Latin hypercube samples is proposed for vector means.