## Annals of Statistics

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

### A classification criterion for definitive screening designs

Eric D. Schoen, Pieter T. Eendebak, and Peter Goos

#### 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**

Received: January 2018

Revised: May 2018

First available in Project Euclid: 11 January 2019

**Permanent link to this document**

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

**Digital Object Identifier**

doi:10.1214/18-AOS1723

**Mathematical Reviews number (MathSciNet)**

MR3909964

**Zentralblatt MATH identifier**

07033165

**Subjects**

Primary: 62K20: Response surface designs

Secondary: 05B20: Matrices (incidence, Hadamard, etc.) 94C30: Applications of design theory [See also 05Bxx]

**Keywords**

Conference matrix isomorphism class $J_{4}$-characteristic projection

#### 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

#### 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.Digital Object Identifier: doi:10.1214/18-AOS1723SUPPSupplemental files are immediately available to subscribers. Non-subscribers gain access to supplemental files with the purchase of the article.