An adaptive composite quantile approach to dimension reduction

TL;DR

This paper introduces an adaptive composite quantile method for dimension reduction in multivariate regression, which is robust, efficient, and capable of uncovering all relevant directions with minimal assumptions.

Contribution

It proposes a novel adaptive composite quantile approach that improves upon existing methods by being robust, assumption-minimal, and fully capable of revealing all dimension reduction directions.

Findings

Method is robust against outliers.

It requires minimal assumptions.

Numerical examples demonstrate effectiveness.

Abstract

Sufficient dimension reduction [J. Amer. Statist. Assoc. 86 (1991) 316-342] has long been a prominent issue in multivariate nonparametric regression analysis. To uncover the central dimension reduction space, we propose in this paper an adaptive composite quantile approach. Compared to existing methods, (1) it requires minimal assumptions and is capable of revealing all dimension reduction directions; (2) it is robust against outliers and (3) it is structure-adaptive, thus more efficient. Asymptotic results are proved and numerical examples are provided, including a real data analysis.