Open Access
2023 Construction of maximin L1-distance Latin hypercube designs
Yuhao Yin, Lin Wang, Hongquan Xu
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Electron. J. Statist. 17(2): 3942-3968 (2023). DOI: 10.1214/23-EJS2194


Computer experiments are increasingly being used to build high-quality surrogate models for complex emulation systems. Maximin distance Latin hypercube design is an efficient approach for designing computer experiments. Algorithmic search is commonly used for finding such designs but becomes ineffective when searching for large designs. Theoretical construction of such designs is fast but limited and challenging. In this paper, we propose a series of construction methods for maximin distance Latin hypercube designs. We use a piece-wise linear transformation to obtain balanced designs which are then rotated to generate Latin hypercube designs. Theoretical results guarantee that the generated designs are asymptotically optimal under the maximin distance criterion. The generated designs also exhibit low column correlations and mirror symmetry, which significantly benefits the identification of the main and interaction effects. Moreover, we present numerical comparisons with existing methods to demonstrate the superiority of the proposed methods.


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Yuhao Yin. Lin Wang. Hongquan Xu. "Construction of maximin L1-distance Latin hypercube designs." Electron. J. Statist. 17 (2) 3942 - 3968, 2023.


Received: 1 August 2023; Published: 2023
First available in Project Euclid: 11 December 2023

Digital Object Identifier: 10.1214/23-EJS2194

Primary: 62K99
Secondary: 62K15

Keywords: computer experiment , Correlation , factorial design , orthogonal array , space-filling design

Vol.17 • No. 2 • 2023
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