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August 2014 On the construction of nested space-filling designs
Fasheng Sun, Min-Qian Liu, Peter Z. G. Qian
Ann. Statist. 42(4): 1394-1425 (August 2014). DOI: 10.1214/14-AOS1229


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.


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Fasheng Sun. Min-Qian Liu. Peter Z. G. Qian. "On the construction of nested space-filling designs." Ann. Statist. 42 (4) 1394 - 1425, August 2014.


Published: August 2014
First available in Project Euclid: 25 June 2014

zbMATH: 1297.62178
MathSciNet: MR3226161
Digital Object Identifier: 10.1214/14-AOS1229

Primary: 62K15
Secondary: 62K20

Keywords: computer experiment , difference matrix , Galois field , OA-based Latin hypercube , orthogonal array , Rao–Hamming construction , sliced space-filling design

Rights: Copyright © 2014 Institute of Mathematical Statistics


Vol.42 • No. 4 • August 2014
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