### Abstract

Supersaturated designs are useful for factor screening experiments under the factor sparsity assumption that only a small number of factors are active. The popular E(s^{2})-criterion for choosing two-level supersaturated designs minimizes the sum of squares of theentries of the information matrix over the designs in which the two levels of each factor appear equal number of times. Jones and Majumdar (2014) proposed the UE(s^{2})-criterion which is essentially the same as the E(s^{2})-criterion except that the requirement of factor-level-balance is dropped. Removing this constraint makes UE(s^{2})-optimal designs easy to construct, but it also produces many UE(s^{2})-optimal designs with diverse performances. It is necessary to choose better designs from them, especially those with good lower-dimensional projection properties. While E(s^{2})-optimal designs tend to have better lower-dimensional projections than arbitrary UE(s^{2})-optimal designs, they are usually very difficult to construct. We propose a secondary criterion and provide simple and systematic constructions of superior UE(s^{2})-optimal designs having good projection properties. We also derive conditions under which E(s^{2})-optimal designs are UE(s^{2})-optimal as well and identify several families of designs that are optimal under both criteria.

Original language | English |
---|---|

Pages (from-to) | 105-114 |

Number of pages | 10 |

Journal | Journal of Statistical Planning and Inference |

Volume | 196 |

DOIs | |

Publication status | Published - 2018 Aug |

### Fingerprint

### Keywords

- Active factor
- Factor sparsity
- Hadamard matrix
- Projection property
- Screening design

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics

### Cite this

^{2})- and UE(s

^{2})-optimal supersaturated designs.

*Journal of Statistical Planning and Inference*,

*196*, 105-114. https://doi.org/10.1016/j.jspi.2017.10.012

**E(s ^{2})- and UE(s^{2})-optimal supersaturated designs.** / Cheng, Ching Shui; Das, Ashish; Singh, Rakhi; Tsai, Pi Wen.

Research output: Contribution to journal › Article

^{2})- and UE(s

^{2})-optimal supersaturated designs',

*Journal of Statistical Planning and Inference*, vol. 196, pp. 105-114. https://doi.org/10.1016/j.jspi.2017.10.012

^{2})- and UE(s

^{2})-optimal supersaturated designs. Journal of Statistical Planning and Inference. 2018 Aug;196:105-114. https://doi.org/10.1016/j.jspi.2017.10.012

}

TY - JOUR

T1 - E(s2)- and UE(s2)-optimal supersaturated designs

AU - Cheng, Ching Shui

AU - Das, Ashish

AU - Singh, Rakhi

AU - Tsai, Pi Wen

PY - 2018/8

Y1 - 2018/8

N2 - Supersaturated designs are useful for factor screening experiments under the factor sparsity assumption that only a small number of factors are active. The popular E(s2)-criterion for choosing two-level supersaturated designs minimizes the sum of squares of theentries of the information matrix over the designs in which the two levels of each factor appear equal number of times. Jones and Majumdar (2014) proposed the UE(s2)-criterion which is essentially the same as the E(s2)-criterion except that the requirement of factor-level-balance is dropped. Removing this constraint makes UE(s2)-optimal designs easy to construct, but it also produces many UE(s2)-optimal designs with diverse performances. It is necessary to choose better designs from them, especially those with good lower-dimensional projection properties. While E(s2)-optimal designs tend to have better lower-dimensional projections than arbitrary UE(s2)-optimal designs, they are usually very difficult to construct. We propose a secondary criterion and provide simple and systematic constructions of superior UE(s2)-optimal designs having good projection properties. We also derive conditions under which E(s2)-optimal designs are UE(s2)-optimal as well and identify several families of designs that are optimal under both criteria.

AB - Supersaturated designs are useful for factor screening experiments under the factor sparsity assumption that only a small number of factors are active. The popular E(s2)-criterion for choosing two-level supersaturated designs minimizes the sum of squares of theentries of the information matrix over the designs in which the two levels of each factor appear equal number of times. Jones and Majumdar (2014) proposed the UE(s2)-criterion which is essentially the same as the E(s2)-criterion except that the requirement of factor-level-balance is dropped. Removing this constraint makes UE(s2)-optimal designs easy to construct, but it also produces many UE(s2)-optimal designs with diverse performances. It is necessary to choose better designs from them, especially those with good lower-dimensional projection properties. While E(s2)-optimal designs tend to have better lower-dimensional projections than arbitrary UE(s2)-optimal designs, they are usually very difficult to construct. We propose a secondary criterion and provide simple and systematic constructions of superior UE(s2)-optimal designs having good projection properties. We also derive conditions under which E(s2)-optimal designs are UE(s2)-optimal as well and identify several families of designs that are optimal under both criteria.

KW - Active factor

KW - Factor sparsity

KW - Hadamard matrix

KW - Projection property

KW - Screening design

UR - http://www.scopus.com/inward/record.url?scp=85043227184&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85043227184&partnerID=8YFLogxK

U2 - 10.1016/j.jspi.2017.10.012

DO - 10.1016/j.jspi.2017.10.012

M3 - Article

AN - SCOPUS:85043227184

VL - 196

SP - 105

EP - 114

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

SN - 0378-3758

ER -