2020/02/12 by Abdul‐Nasah Soale, Soale, Abdul-Nasah, Yuexiao Dong +1
Engineering · Mathematics · #Control Systems and Identification #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Sparse and Compressive Sensing Techniques #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2002.05264
openalex publication_date 2020/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we introduce principal asymmetric least squares (PALS) as a unified framework for linear and nonlinear sufficient dimension reduction. Classical methods such as sliced inverse regression (Li, 1991) and principal support vector machines (Li, Artemiou and Li, 2011) may not perform well in the presence of heteroscedasticity, while our proposal addresses this limitation by synthesizing different expectile levels. Through extensive numerical studies, we demonstrate the superior performance of PALS in terms of both computation time and estimation accuracy. For the asymptotic analysis of PALS for linear sufficient dimension reduction, we develop new tools to compute the derivative of an expectation of a non-Lipschitz function.