On sufficient dimension reduction via principal asymmetric least squares

Abdul-Nasah Soale and Yuexiao Dong

Journal of Nonparametric Statistics, 2022, vol. 34, issue 1, 77-94

Abstract: Principal asymmetric least squares (PALS) is introduced as a novel method for sufficient dimension reduction with heteroscedastic error. Classical methods such as MAVE [Xia et al. (2002), ‘An Adaptive Estimation of Dimension Reduction Space’ (with discussion), Journal of the Royal Statistical Society Series B, 64, 363–410] and PSVM [Li et al. (2011), ‘Principal Support Vector Machines for Linear and Nonlinear Sufficient Dimension Reduction’, The Annals of Statistics, 39, 3182–3210] may not perform well in the presence of heteroscedasticity, while the new proposal addresses this limitation by synthesising different expectile levels. Through extensive numerical studies, we demonstrate the superior performance of PALS in terms of estimation accuracy over classical methods including MAVE and PSVM. For the asymptotic analysis of PALS, we develop new tools to compute the derivative of an expectation of a non-Lipschitz function.

Date: 2022
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DOI: 10.1080/10485252.2021.2025237

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