Minimum aberration majorization in non-isomorphic saturated designs

Kai Tai Fang; Aijun Zhang

doi:10.1016/j.jspi.2003.07.015

Minimum aberration majorization in non-isomorphic saturated designs

Kai Tai Fang^*, Aijun Zhang

^*Corresponding author for this work

Department of Mathematics

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

7 Citations (Scopus)

Abstract

In this paper we propose a new criterion, minimum aberration majorization, for comparing non-isomorphic saturated designs. This criterion is based on the generalized word-length pattern proposed by Ma and Fang (Metrika 53 (2001) 85) and Xu and Wu (Ann. Statist. 29 (2001) 1066) and majorization theory. The criterion has been successfully applied to check non-isomorphism and rank order saturated designs. Examples are given through five non-isomorphic L₁₆(2¹⁵) designs and two L₂₇(3¹³) designs.

Original language	English
Pages (from-to)	337-346
Number of pages	10
Journal	Journal of Statistical Planning and Inference
Volume	126
Issue number	1
DOIs	https://doi.org/10.1016/j.jspi.2003.07.015
Publication status	Published - 1 Nov 2004

Scopus Subject Areas

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

User-Defined Keywords

Aberration
Isomorphism
Majorization
Saturated design

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10.1016/j.jspi.2003.07.015

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title = "Minimum aberration majorization in non-isomorphic saturated designs",

abstract = "In this paper we propose a new criterion, minimum aberration majorization, for comparing non-isomorphic saturated designs. This criterion is based on the generalized word-length pattern proposed by Ma and Fang (Metrika 53 (2001) 85) and Xu and Wu (Ann. Statist. 29 (2001) 1066) and majorization theory. The criterion has been successfully applied to check non-isomorphism and rank order saturated designs. Examples are given through five non-isomorphic L16(215) designs and two L27(313) designs.",

keywords = "Aberration, Isomorphism, Majorization, Saturated design",

author = "Fang, {Kai Tai} and Aijun Zhang",

note = "Funding Information: The authors would like to thank Professor F.J. Hickernell, Professor R. Mukerjee, Dr. M.Q. Liu, Dr. H. Qin and referees for their valuable suggestions and comments. This work was partially supported by the Hong Kong RGC Grant RGC/HKBU 2044/02P.",

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T1 - Minimum aberration majorization in non-isomorphic saturated designs

AU - Fang, Kai Tai

AU - Zhang, Aijun

N1 - Funding Information: The authors would like to thank Professor F.J. Hickernell, Professor R. Mukerjee, Dr. M.Q. Liu, Dr. H. Qin and referees for their valuable suggestions and comments. This work was partially supported by the Hong Kong RGC Grant RGC/HKBU 2044/02P.

PY - 2004/11/1

Y1 - 2004/11/1

N2 - In this paper we propose a new criterion, minimum aberration majorization, for comparing non-isomorphic saturated designs. This criterion is based on the generalized word-length pattern proposed by Ma and Fang (Metrika 53 (2001) 85) and Xu and Wu (Ann. Statist. 29 (2001) 1066) and majorization theory. The criterion has been successfully applied to check non-isomorphism and rank order saturated designs. Examples are given through five non-isomorphic L16(215) designs and two L27(313) designs.

AB - In this paper we propose a new criterion, minimum aberration majorization, for comparing non-isomorphic saturated designs. This criterion is based on the generalized word-length pattern proposed by Ma and Fang (Metrika 53 (2001) 85) and Xu and Wu (Ann. Statist. 29 (2001) 1066) and majorization theory. The criterion has been successfully applied to check non-isomorphism and rank order saturated designs. Examples are given through five non-isomorphic L16(215) designs and two L27(313) designs.

KW - Aberration

KW - Isomorphism

KW - Majorization

KW - Saturated design

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U2 - 10.1016/j.jspi.2003.07.015

DO - 10.1016/j.jspi.2003.07.015

M3 - Journal article

AN - SCOPUS:4444330251

SN - 0378-3758

VL - 126

SP - 337

EP - 346

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

IS - 1

ER -

Minimum aberration majorization in non-isomorphic saturated designs

Abstract

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