On expectile-assisted inverse regression estimation for sufficient dimension reduction

Moment-based sufficient dimension reduction methods such as sliced inverse regression may not work well in the presence of heteroscedasticity. We propose to first estimate the expectiles through kernel expectile regression, and then carry out dimension reduction based on random projections of the regression expectiles. Several popular inverse regression methods in the literature are extended under this general framework. The proposed expectile-assisted methods outperform existing moment-based dimension reduction methods in both numerical studies and an analysis of the Big Mac data.