A1208
Title: Minimax designs for misspecified linear models with $L_{\infty}$-norm bounded departures
Authors: Shaohua Xu - Zhongnan University of Economics and Law (China) [presenting]
Yongdao Zhou - Nankai University (China)
Zheng Zhou - Beijing University of Technology (China)
Abstract: Misspecified linear models offer flexibility for real-world data departing from strict linearity. Minimax designs ensure robust performance under model misspecification. For continuous design spaces, most existing minimax designs within the $L_2$-neighborhood require absolute continuity with respect to the Lebesgue measure, while the $L_\infty$-neighborhood allows broader candidate designs but presents significant challenges. Current $L_\infty$-based minimax designs are limited to restricted spaces, lacking true robustness. Minimax designs are constructed for both ordinary least squares (OLS) and inverse probability weighted (IPW) estimators under the $L_\infty$-neighborhood. Specifically, for multiple linear regression without interactions defined over $[0,1]^{d}$, the minimax design for the OLS estimator is a mixture of the full factorial and continuous uniform designs. In addition, the minimax design for the OLS estimator outperforms that for the IPW estimator if and only if the $L_\infty$-bound is below a critical value. Simulations confirm that the proposed designs outperform existing ones under model misspecification.
