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**Large sample properties of simulations using Latin hypercube sampling.**
*(English)*
Zbl 0627.62010

Latin hypercube sampling [see M. D. McKay, W. J. Conover and R. J. Beckman, Technometrics 21, 239-245 (1979; Zbl 0415.62011)] is a method of sampling that can be used to produce input values for estimation of expectations of functions of output variables. Let \(X=(X_ 1,...,X_ N)\) be a random vector of fixed length K, and h(X) a function the expected value of which is to be estimated by the mean value \(\bar h=N^{-1}\sum^{N}_{j=1}h(X_ j)\) for a sample \(X_ 1,...,X_ N\). The Latin hypercube sampling to generate \(X_ 1,...,X_ N\), is described. The asymptotic variance of such an estimate is obtained.

As long as N is large compared with K, Latin hypercube sampling gives an estimator with lower variance than simple random sampling for any function h(.) having finite second moment.

The estimate is also shown to be asymptotically normal. Asymptotically, the variance is less than that obtained using simple random sampling, with the degree of variance reduction depending on the degree of additivity in the function being integrated. A method for producing Latin hypercube samples when the components of the input variables are statistically dependent is also described. These techniques are applied to a simulation of the performance of an impact printer actuator modeled by a set of differential equations.

Comparing simple random sampling to Latin hypercube sampling, both with sample sizes of 100, the latter one produced considerable reductions in variance (22% to 69% in four cases).

As long as N is large compared with K, Latin hypercube sampling gives an estimator with lower variance than simple random sampling for any function h(.) having finite second moment.

The estimate is also shown to be asymptotically normal. Asymptotically, the variance is less than that obtained using simple random sampling, with the degree of variance reduction depending on the degree of additivity in the function being integrated. A method for producing Latin hypercube samples when the components of the input variables are statistically dependent is also described. These techniques are applied to a simulation of the performance of an impact printer actuator modeled by a set of differential equations.

Comparing simple random sampling to Latin hypercube sampling, both with sample sizes of 100, the latter one produced considerable reductions in variance (22% to 69% in four cases).

Reviewer: J.Tankó