ABSTRACT
We propose a principal single-index varying-coefficient model focusing on conditional quantiles. In this general and flexible class of models, dimension reduction is achieved in three aspects: first, standard varying-coefficient models can partially avoid curse of dimensionality of large dimensional nonparametric regression; second, a one-dimensional adaptive index is constructed from multiple index variables; finally, the number of independent functions is further reduced by using principal functions. We derive the convergence rate of the estimates and asymptotic normality of the index parameter and the coefficient functions. Penalization can be added straightforwardly to obtain joint variable selection and dimension reduction. Simulations are used to demonstrate the performances and an empirical application is presented.
Acknowledgments
The authors want to thank the Editor, an associate editor and anonymous reviewers for their comments that greatly improved the paper.
Disclosure statement
No potential conflict of interest was reported by the authors.