Abstract: Nested Latin hypercube designs (Qian (2009)) and sliced Latin hypercube designs (Qian (2012)) are extensions of ordinary Latin hypercube designs with special combinational structures. It is known that the mean estimator over the unit cube computed from either of these designs has the same asymptotic variance as its counterpart for an ordinary Latin hypercube design. We derive a central limit theorem to show that the mean estimator of either of these two designs has a limiting normal distribution. This result is useful for making confidence statements for such designs in numerical integration, uncertainty quantification, and sensitivity analysis.

Key words and phrases: Computer experiment, design of experiment, method of moments, numerical integration, uncertainty quantification.