## Annals of Statistics

### A classification criterion for definitive screening designs

#### Abstract

A conference design is a rectangular matrix with orthogonal columns, one zero in each column, at most one zero in each row and $-1$’s and $+1$’s elsewhere. A definitive screening design can be constructed by folding over a conference design and adding a row vector of zeroes. We prove that, for a given even number of rows, there is just one isomorphism class for conference designs with two or three columns. Next, we derive all isomorphism classes for conference designs with four columns. Based on our results, we propose a classification criterion for definitive screening designs founded on projections into four factors. We illustrate the potential of the criterion by studying designs with 24 and 82 factors.

#### Article information

Source
Ann. Statist., Volume 47, Number 2 (2019), 1179-1202.

Dates
Revised: May 2018
First available in Project Euclid: 11 January 2019

https://projecteuclid.org/euclid.aos/1547197252

Digital Object Identifier
doi:10.1214/18-AOS1723

Mathematical Reviews number (MathSciNet)
MR3909964

Zentralblatt MATH identifier
07033165

#### Citation

Schoen, Eric D.; Eendebak, Pieter T.; Goos, Peter. A classification criterion for definitive screening designs. Ann. Statist. 47 (2019), no. 2, 1179--1202. doi:10.1214/18-AOS1723. https://projecteuclid.org/euclid.aos/1547197252

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#### Supplemental materials

• Conference matrices of order 82. We provide Matlab code to construct the 26 nonisomorphic conference matrices of order 82 from Hurkens and Seidel (1985) and to evaluate the $F_{4}$ vector of the definitive screening designs with 82 factors based on these matrices.