On the construction of nested space-filling designs
Fasheng Sun, Min-Qian Liu, Peter Z. G. Qian
The Annals of Statistics · 2014 · Volume 42 · Issue 4
Abstract
Nested space-filling designs are nested designs with attractive low-dimensional stratification. Such designs are gaining popularity in statistics, applied mathematics and engineering. Their applications include multi-fidelity computer models, stochastic optimization problems, multi-level fitting of nonparametric functions, and linking parameters. We propose methods for constructing several new classes of nested space-filling designs. These methods are based on a new group projection and other algebraic techniques. The constructed designs can accommodate a nested structure with an arbitrary number of layers and are more flexible in run size than the existing families of nested space-filling designs. As a byproduct, the proposed methods can also be used to obtain sliced space-filling designs that are appealing for conducting computer experiments with both qualitative and quantitative factors.
Keywords
62K15, 62K20, computer experiment, difference matrix, Galois field, OA-based Latin hypercube, orthogonal array, Rao–Hamming construction, sliced space-filling design
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