Maximin sliced latin hypercube designs with application to cross validating prediction error

This paper introduces an approach to construct a new type of design, called a maximin sliced Latin hypercube design. This design is a special type of Latin hypercube design that can be partitioned into smaller slices of Latin hypercube designs, where both the whole design and each slice are optimal under the maximin criterion. To construct these designs, a two-step construction method for generating sliced Latin hypercubes is proposed. Several examples are presented to evaluate the performance of the algorithm. An application of this type of optimal design in estimating prediction error by cross validation is also illustrated here.