On expectile-assisted inverse regression estimation for sufficient dimension reduction

TL;DR

This paper introduces expectile-assisted inverse regression methods for sufficient dimension reduction, which outperform traditional moment-based methods especially under heteroscedasticity, by leveraging kernel expectile regression and random projections.

Contribution

It proposes a novel framework combining expectile estimation with inverse regression, extending existing methods and improving performance in heteroscedastic settings.

Findings

Outperforms existing methods in numerical studies

Effective in heteroscedastic data scenarios

Demonstrated success on Big Mac data analysis

Abstract

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.