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Controlling correlations in latin hypercube samples. (English) Zbl 0813.65060
This paper presents a method of controlling the correlations among the variables to reduce the variance of Monte Carlo integrals. Motivated by R. L. Iman and W. J. Conover’s latin hypercube sampling (LHS) with rank correlation [Commun. Stat., Simulation Comput. 11, 311-334 (1982; Zbl 0496.65071)], the author proposes the ranked Gram-Schmidt (RGS) algorithm. Simulation studies for \(10 \leq n \leq 500\) indicate that the RGS method produces latin hypercube samples with correlations of order \(O_ p (n^{-3/2})\) among input samples and that it provides more successful results at reducing correlations than the Iman and Conover’s method. An analysis of the algorithm provides a reason of this finding and lower bounds for the magnitude of the correlation.
Reviewer: K.Uosaki (Tottori)

65D32 Numerical quadrature and cubature formulas
65C99 Probabilistic methods, stochastic differential equations
65C05 Monte Carlo methods
62H20 Measures of association (correlation, canonical correlation, etc.)
62J10 Analysis of variance and covariance (ANOVA)
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