Efficient computational algorithms for approximate optimal designs

In this paper, we propose two simple yet efficient computational algorithms to obtain approximate optimal designs for multi-dimensional linear regression on a large variety of design spaces. We focus on the two commonly used optimal criteria, D- and A-optimal criteria. For D-optimality, we provide a...

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Bibliographic Details
Published in:	Journal of statistical computation and simulation Vol. 92; no. 4; pp. 764 - 793
Main Authors:	Duan, Jiangtao, Gao, Wei, Ma, Yanyuan, Ng, Hon Keung Tony
Format:	Journal Article
Language:	English
Published:	Taylor & Francis 04.03.2022
Subjects:	A-optimal Approximate experimental design D-optimal Regression model
ISSN:	0094-9655, 1563-5163
Online Access:	Get full text
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Summary:	In this paper, we propose two simple yet efficient computational algorithms to obtain approximate optimal designs for multi-dimensional linear regression on a large variety of design spaces. We focus on the two commonly used optimal criteria, D- and A-optimal criteria. For D-optimality, we provide an alternative proof for the monotonic convergence for D-optimal criterion and propose an efficient computational algorithm to obtain the approximate D-optimal design. We further show that the proposed algorithm converges to the D-optimal design and then proves that the approximate D-optimal design converges to the continuous D-optimal design under certain conditions. For A-optimality, we provide an efficient algorithm to obtain approximate A-optimal design and conjecture the monotonicity of the proposed algorithm. Numerical comparisons suggest that the proposed algorithms perform well and they are comparable or superior to some existing algorithms.
ISSN:	0094-9655 1563-5163
DOI:	10.1080/00949655.2021.1974439