## The Annals of Statistics

### Uniform projection designs

#### 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.

#### Article information

Source
Ann. Statist., Volume 47, Number 1 (2019), 641-661.

Dates
Revised: March 2018
First available in Project Euclid: 30 November 2018

https://projecteuclid.org/euclid.aos/1543568601

Digital Object Identifier
doi:10.1214/18-AOS1705

Mathematical Reviews number (MathSciNet)
MR3909945

Zentralblatt MATH identifier
07036214

#### Citation

Sun, Fasheng; Wang, Yaping; Xu, Hongquan. Uniform projection designs. Ann. Statist. 47 (2019), no. 1, 641--661. doi:10.1214/18-AOS1705. https://projecteuclid.org/euclid.aos/1543568601

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