Abstract: Latin hypercube designs have recently found wide applications both in design of experiments and in numerical integration. An important property of this class of designs is that they achieve uniformity in each univariate margin. In this article we study the use of correlation criteria to select a Latin hypercube. We introduce the polynomial canonical correlation of two vectors and argue that a design which has a small polynomial canonical correlation for each pair of its columns is preferred. An algorithm for reducing polynomial canonical correlations of a Latin hypercube is developed. The implementation of the algorithm is discussed, and its performance investigated. Comparison with Owen's algorithm is also made.
Key words and phrases: Canonical correlation, computer experiments, exploratory designs.