  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.
