On Latin hypercube sampling. (English) Zbl 0867.62005

Loh, Wei-Liem

Ann. Stat. 24, No. 5, 2058-2080 (1996).

Summary: 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 \(\widehat{\mu}_n\) based on a Latin hypercube sample. The second establishes sufficient conditions on the convergence rate in the strong law for \(\widehat{\mu}_n\). 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.

MSC:

62D05	Sampling theory, sample surveys
62G15	Nonparametric tolerance and confidence regions
62E20	Asymptotic distribution theory in statistics
60F05	Central limit and other weak theorems
60F15	Strong limit theorems

Keywords:

Stein’s method; strong law of large numbers; Latin hypercube sampling; Berry-Esseen-type bound; multivariate central limit theorem; sample mean; convergence rate; strong law; empirical likelihood; confidence regions