The Annals of Statistics

On the construction of nested space-filling designs

Fasheng Sun, Min-Qian Liu, and Peter Z. G. Qian

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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.

Article information

Ann. Statist., Volume 42, Number 4 (2014), 1394-1425.

First available in Project Euclid: 25 June 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62K15: Factorial designs
Secondary: 62K20: Response surface designs

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


Sun, Fasheng; Liu, Min-Qian; Qian, Peter Z. G. On the construction of nested space-filling designs. Ann. Statist. 42 (2014), no. 4, 1394--1425. doi:10.1214/14-AOS1229.

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