This paper concerns robust and efficient direction identification for a group-
wise additive multiple-index model, in which each additive function has a single-index
structure. Interestingly, without involving non-parametric approach, we show that the
directions of all the index parameter vectors can be recovered by a simple linear
composite quantile regression (CQR). As a specific application, a iterative-free CQR
estimation procedure for the partially linear single-index model is proposed. Further-
more, it can also be used to develop a penalized CQR procedure for variable selection
in the high-dimensional settings. The new method has superiority in robustness and
efficiency by inheriting the advantage of the CQR approach. Simulation results and
real-data analysis also confirm our method.

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• Robust and efficient direction identification for groupwise additive multiple-index models and its applications