On Latin hypercube sampling. (English) Zbl 0867.62005

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.


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
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