Multiple Quantile Modelling via Reduced Rank Regression

Heng Lian, Weihua Zhao, Yanyuan Ma
2019 Statistica sinica  
Since quantile regression estimator at a fixed quantile level mainly relies on a small subset of the observed data, efforts have been made to construct simultaneous estimation at multiple quantile levels in order to take full advantage of all the observations and improve estimation efficiency. We propose a novel approach that links multiple linear quantile models through imposing a condition on the rank of the matrix formed by all the regression parameters. The approach has the flavor of the
more » ... uced rank regression while also shares similarity to the dimension reduction modeling. We develop estimation and inference tools in such models and also study the optimality in terms of asymptotic estimation variance. Simulation experiments are conducted to examine the numerical performance of the proposed procedure. The method is further illustrated in a data example.
doi:10.5705/ss.202016.0426 fatcat:ysf7lr434vh7bb7pcvjbajykgq