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A central limit theorem for nested or sliced Latin hypercube designs. (English) Zbl 1356.62101
Summary: Nested Latin hypercube designs [P. Z. G. Qian, Biometrika 96, No. 4, 957–970 (2009; Zbl 1179.62103)] and sliced Latin hypercube designs [P. Z. G. Qian, J. Am. Stat. Assoc. 107, No. 497, 393–399 (2012; Zbl 1261.62073)] 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.

62K15 Factorial statistical designs
05B15 Orthogonal arrays, Latin squares, Room squares
60F05 Central limit and other weak theorems
68U20 Simulation (MSC2010)
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