On performance of correlation control methods in simulation of random vectors defined by marginals and covariances

Abstract eng:
The objective of this paper is a study of performance of correlation control of recently proposed procedure for sampling from a multivariate population within the framework of Monte Carlo simulations (especially Latin Hypercube Sampling). In particular, we study the ability of the method to fulfill the prescribed correlation structure of a random vector for various sample sizes and number of marginal variables. Two norms of correlation error are defined, one very conservative and related to extreme errors, other related to averages of correlation errors. We study behavior of Pearson correlation coefficient for Gaussian vectors and Spearman rank order coefficient. Theoretical results on performance bounds for both correlation types in the case of desired uncorrelatedness are compared to performance of the proposed technique and also to other previously developed techniques for correlation control, namely the Cholesky orthogonalization as applied by Iman and Conover (1980,1982); and Gram-Schmidt orthogonalization used by Owen (1994).

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