On Sufficient Dimension Reduction via Principal Asymmetric Least Squares

• Activity Number: 496 - Dimension Reduction
• Type: Contributed
• Date/Time: Thursday, August 6, 2020 : 10:00 AM to 2:00 PM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Abdul-Nasah Soale* and Yuexiao Dong
• Companies: Temple University and Temple University
• Keywords: expectile regression; heteroscedasticity; distance correlation; nonlinear dimension reduction

Abstract

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.