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February 2019 Uniform projection designs
Fasheng Sun, Yaping Wang, Hongquan Xu
Ann. Statist. 47(1): 641-661 (February 2019). DOI: 10.1214/18-AOS1705

Abstract

Efficient designs are in high demand in practice for both computer and physical experiments. Existing designs (such as maximin distance designs and uniform designs) may have bad low-dimensional projections, which is undesirable when only a few factors are active. We propose a new design criterion, called uniform projection criterion, by focusing on projection uniformity. Uniform projection designs generated under the new criterion scatter points uniformly in all dimensions and have good space-filling properties in terms of distance, uniformity and orthogonality. We show that the new criterion is a function of the pairwise $L_{1}$-distances between the rows, so that the new criterion can be computed at no more cost than a design criterion that ignores projection properties. We develop some theoretical results and show that maximin $L_{1}$-equidistant designs are uniform projection designs. In addition, a class of asymptotically optimal uniform projection designs based on good lattice point sets are constructed. We further illustrate an application of uniform projection designs via a multidrug combination experiment.

Citation

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Fasheng Sun. Yaping Wang. Hongquan Xu. "Uniform projection designs." Ann. Statist. 47 (1) 641 - 661, February 2019. https://doi.org/10.1214/18-AOS1705

Information

Received: 1 January 2018; Revised: 1 March 2018; Published: February 2019
First available in Project Euclid: 30 November 2018

zbMATH: 07036214
MathSciNet: MR3909945
Digital Object Identifier: 10.1214/18-AOS1705

Subjects:
Primary: 62K15, 62K99

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.47 • No. 1 • February 2019
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