Constructing K-optimal designs for regression models

Zongzhi Yue, Xiaoqing Zhang, P. van den Driessche and Julie Zhou ()
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Zongzhi Yue: University of Victoria
Xiaoqing Zhang: University of Victoria
P. van den Driessche: University of Victoria
Julie Zhou: University of Victoria

Statistical Papers, 2023, vol. 64, issue 1, No 10, 205-226

Abstract: Abstract We study approximate K-optimal designs for various regression models by minimizing the condition number of the information matrix. This minimizes the error sensitivity in the computation of the least squares estimator of regression parameters and also avoids the multicollinearity in regression. Using matrix and optimization theory, we derive several theoretical results of K-optimal designs, including convexity of K-optimality criterion, lower bounds of the condition number, and symmetry properties of K-optimal designs. A general numerical method is developed to find K-optimal designs for any regression model on a discrete design space. In addition, specific results are obtained for polynomial, trigonometric and second-order response models.

Keywords: Optimal regression design; Fourier regression; Condition number; Convex optimization; Matrix norm; Second-order response model; 62K05; 15A18 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s00362-022-01317-9

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