Block-circulant matrices for constructing optimal Latin hypercube designs

• Published in: Journal of statistical planning and inference Vol. 141; no. 5; pp. 1933 - 1943
• Main Authors: Georgiou, S.D., Stylianou, S.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier B.V 01-05-2011; Elsevier
• Subjects: Autocorrelation function; Circulant matrices; Combinatorics; Combinatorics. Ordered structures; Designs and configurations; Exact sciences and technology; Experimental design; Factorial design; General topics; Latin hypercube design with low correlation; Mathematics; Multivariate analysis; Orthogonal Latin hypercube design; Probability and statistics; Sciences and techniques of general use; Statistics; Autocorrelation function; Orthogonal Latin hypercube design; Factorial design; Circulant matrices; Latin hypercube design with low correlation; Orthogonal design; Correlation; Computer simulation; Periodic function; Statistical association; Statistical decision; Multivariate analysis; Statistical simulation; Orthogonal polynomial; Statistical method; Block design; Correlation analysis; Experimental design; Hypercube; Optimal design(statistics); Mathematical expansion; Expansion; Block matrix
• ISSN: 0378-3758; 1873-1171
• DOI: 10.1016/j.jspi.2010.12.006

Computer simulations are usually needed to study a complex physical process. In this paper, we propose new procedures for constructing orthogonal or low-correlation block-circulant Latin hypercube designs. The basic concept of these methods is to use vectors with a constant periodic autocorrelation function to obtain suitable block-circulant Latin hypercube designs. A general procedure for constructing orthogonal Latin hypercube designs with favorable properties and allowing run sizes being different from a power of 2 (or a power of 2 plus 1), is presented here for the first time. In addition, an expansion of the method is given for constructing Latin hypercube designs with low correlation. This expansion is useful when orthogonal Latin hypercube designs do not exist. The properties of the generated designs are further investigated. Some examples of the new designs, as generated by the proposed procedures, are tabulated. In addition, a brief comparison with the designs that appear in the literature is given.