Nearly orthogonal latin hypercube designs for many design columns

Lin Wang; Jian Feng Yang; Dennis K.J. Lin; Min Qian Liu

doi:10.5705/ss.2014.160

Nearly orthogonal latin hypercube designs for many design columns

Lin Wang, Jian Feng Yang, Dennis K.J. Lin, Min Qian Liu

Statistics

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

Latin hypercube designs (LHDs) have found wide applications in computer experiments. Some methods have been proposed to construct orthogonal (or nearly orthogonal) LHDs. This paper proposes methods for expanding a fold-over orthogonal (or nearly orthogonal) LHD to a nearly orthogonal LHD which is able to accommodate many factors. The number of factors is flexible and can be almost as twice large as the number of factors of the original LHD, while the run size remains unchanged. It is shown that the upper bound of the maximum correlation between any two distinct columns of the resulting design is very small (smaller than 0.10 for most cases). The proposed methods can be applied to any fold-over LHDs.

Original language	English (US)
Pages (from-to)	1599-1612
Number of pages	14
Journal	Statistica Sinica
Volume	25
Issue number	4
DOIs	https://doi.org/10.5705/ss.2014.160
State	Published - Oct 2015

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

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10.5705/ss.2014.160

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@article{585edfd1221c474d97864dcee2fec3ce,

title = "Nearly orthogonal latin hypercube designs for many design columns",

abstract = "Latin hypercube designs (LHDs) have found wide applications in computer experiments. Some methods have been proposed to construct orthogonal (or nearly orthogonal) LHDs. This paper proposes methods for expanding a fold-over orthogonal (or nearly orthogonal) LHD to a nearly orthogonal LHD which is able to accommodate many factors. The number of factors is flexible and can be almost as twice large as the number of factors of the original LHD, while the run size remains unchanged. It is shown that the upper bound of the maximum correlation between any two distinct columns of the resulting design is very small (smaller than 0.10 for most cases). The proposed methods can be applied to any fold-over LHDs.",

author = "Lin Wang and Yang, {Jian Feng} and Lin, {Dennis K.J.} and Liu, {Min Qian}",

note = "Funding Information: The authors thank Editor Naisyin Wang, an associate editor, and two referees for their valuable comments and suggestions that have resulted in improvements in the paper. This work was supported by the National Natural Science Foundation of China (Grant Nos. 11271205, 11431006, 11101024, 11471172 and 11271355), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20130031110002), and the {"}131{"} Talents Program of Tianjin. The first two authors contributed equally to this work. Publisher Copyright: {\textcopyright} 2015, Institute of Statistical Science. All rights reserved.",

year = "2015",

month = oct,

doi = "10.5705/ss.2014.160",

language = "English (US)",

volume = "25",

pages = "1599--1612",

journal = "Statistica Sinica",

issn = "1017-0405",

publisher = "Institute of Statistical Science",

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T1 - Nearly orthogonal latin hypercube designs for many design columns

AU - Wang, Lin

AU - Yang, Jian Feng

AU - Lin, Dennis K.J.

AU - Liu, Min Qian

N1 - Funding Information: The authors thank Editor Naisyin Wang, an associate editor, and two referees for their valuable comments and suggestions that have resulted in improvements in the paper. This work was supported by the National Natural Science Foundation of China (Grant Nos. 11271205, 11431006, 11101024, 11471172 and 11271355), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20130031110002), and the "131" Talents Program of Tianjin. The first two authors contributed equally to this work. Publisher Copyright: © 2015, Institute of Statistical Science. All rights reserved.

PY - 2015/10

Y1 - 2015/10

N2 - Latin hypercube designs (LHDs) have found wide applications in computer experiments. Some methods have been proposed to construct orthogonal (or nearly orthogonal) LHDs. This paper proposes methods for expanding a fold-over orthogonal (or nearly orthogonal) LHD to a nearly orthogonal LHD which is able to accommodate many factors. The number of factors is flexible and can be almost as twice large as the number of factors of the original LHD, while the run size remains unchanged. It is shown that the upper bound of the maximum correlation between any two distinct columns of the resulting design is very small (smaller than 0.10 for most cases). The proposed methods can be applied to any fold-over LHDs.

AB - Latin hypercube designs (LHDs) have found wide applications in computer experiments. Some methods have been proposed to construct orthogonal (or nearly orthogonal) LHDs. This paper proposes methods for expanding a fold-over orthogonal (or nearly orthogonal) LHD to a nearly orthogonal LHD which is able to accommodate many factors. The number of factors is flexible and can be almost as twice large as the number of factors of the original LHD, while the run size remains unchanged. It is shown that the upper bound of the maximum correlation between any two distinct columns of the resulting design is very small (smaller than 0.10 for most cases). The proposed methods can be applied to any fold-over LHDs.

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JO - Statistica Sinica

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Nearly orthogonal latin hypercube designs for many design columns

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