A note on the semiparametric approach to dimension reduction

Abstract

In this note, we present a theoretical result which relaxes a critical condition required by the semiparametric approach to dimension reduction. The asymptotic normality of the estimators still maintains under weaker assumptions. This improvement greatly increases the applicability of the semiparametric approach.

Keywords:

• Dimension reduction
• semiparametric methods
• estimating equations
• kernel estimation
• sliced inverse regression

Acknowledgments

This article was financially supported by NSERC Discovery Grants (RGPIN 2017 05720 and RGPIN 2018 05846), and National Natural Science Foundation of China 11501005. It has not been published elsewhere and it is not submitted simultaneously for publications elsewhere.