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.

中文翻译：

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用于充分降维的期望辅助逆回归估计

在存在异方差的情况下，基于矩的充分降维方法（例如切片逆回归）可能效果不佳。我们建议首先通过核期望回归估计期望值，然后根据回归期望值的随机投影进行降维。文献中几种流行的逆回归方法都在这个通用框架下进行了扩展。所提出的预期辅助方法在数值研究和巨无霸数据分析中均优于现有的基于矩的降维方法。