E(s2)-Optimality and Minimum Discrepancy in 2-Level Supersaturated Designs

Min Qian Liu; Fred J. Hickernell

E(s²)-Optimality and Minimum Discrepancy in 2-Level Supersaturated Designs

Min Qian Liu, Fred J. Hickernell

Research output: Contribution to journal › Journal article › peer-review

Abstract

Supersaturated experimental designs are often assessed by the E(s²) criterion, and some methods have been found for constructing E(s²)-optimal designs. Another criterion for assessing experimental designs is discrepancy, of which there are several different kinds. The discrepancy measures how much the empirical distribution of the design points deviates from the uniform distribution. Here it is shown that for 2-level supersaturated designs the E(s²) criterion and a certain discrepancy share the same optimal designs.

Original language	English
Pages (from-to)	931-939
Number of pages	9
Journal	Statistica Sinica
Volume	12
Issue number	3
Publication status	Published - Jul 2002
Externally published	Yes

User-Defined Keywords

Hamming distance
reproducing kernel
uniformity

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https://www3.stat.sinica.edu.tw/statistica/j12n3/j12n315/j12n315.htm

Cite this

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title = "E(s2)-Optimality and Minimum Discrepancy in 2-Level Supersaturated Designs",

abstract = "Supersaturated experimental designs are often assessed by the E(s2) criterion, and some methods have been found for constructing E(s2)-optimal designs. Another criterion for assessing experimental designs is discrepancy, of which there are several different kinds. The discrepancy measures how much the empirical distribution of the design points deviates from the uniform distribution. Here it is shown that for 2-level supersaturated designs the E(s2) criterion and a certain discrepancy share the same optimal designs.",

keywords = "Hamming distance, reproducing kernel, uniformity",

author = "Liu, {Min Qian} and Hickernell, {Fred J.}",

note = "Funding information: The authors are grateful to the Editor, an associate editor, and two referees for their valuable comments. Thanks also go to Kai-Tai Fang, Chnag-Xing Ma, Rahul Mukerjee and Guo-Liang Tian for their valuable suggestions and help on this paper. This research was partially supported by Hong Kong Research Council Grant RGC/HKBU/2029/99E, Hong Kong Baptist University Faculty Research Grant FRG/99-00/II-01, and NNSF of China grant 10171051.",

year = "2002",

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AU - Liu, Min Qian

AU - Hickernell, Fred J.

N1 - Funding information: The authors are grateful to the Editor, an associate editor, and two referees for their valuable comments. Thanks also go to Kai-Tai Fang, Chnag-Xing Ma, Rahul Mukerjee and Guo-Liang Tian for their valuable suggestions and help on this paper. This research was partially supported by Hong Kong Research Council Grant RGC/HKBU/2029/99E, Hong Kong Baptist University Faculty Research Grant FRG/99-00/II-01, and NNSF of China grant 10171051.

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N2 - Supersaturated experimental designs are often assessed by the E(s2) criterion, and some methods have been found for constructing E(s2)-optimal designs. Another criterion for assessing experimental designs is discrepancy, of which there are several different kinds. The discrepancy measures how much the empirical distribution of the design points deviates from the uniform distribution. Here it is shown that for 2-level supersaturated designs the E(s2) criterion and a certain discrepancy share the same optimal designs.

AB - Supersaturated experimental designs are often assessed by the E(s2) criterion, and some methods have been found for constructing E(s2)-optimal designs. Another criterion for assessing experimental designs is discrepancy, of which there are several different kinds. The discrepancy measures how much the empirical distribution of the design points deviates from the uniform distribution. Here it is shown that for 2-level supersaturated designs the E(s2) criterion and a certain discrepancy share the same optimal designs.

KW - Hamming distance

KW - reproducing kernel

KW - uniformity

UR - https://www.jstor.org/stable/24307003

M3 - Journal article

SN - 1017-0405

VL - 12

SP - 931

EP - 939

JO - Statistica Sinica

JF - Statistica Sinica

IS - 3

ER -

E(s²)-Optimality and Minimum Discrepancy in 2-Level Supersaturated Designs

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