Composite quantile regression for ultra-high dimensional semiparametric model averaging

To estimate the joint multivariate regression function, a robust ultra-high dimensional semiparametric model averaging approach is developed. Specifically, a three-stage estimation procedure is proposed. In the first step, the joint multivariate function can be approximated by a weighted average of one-dimensional marginal regression functions which can be estimated robustly by the composite quantile marginal regression. In the second step, a nonparametric composite quantile correlation screening technique is proposed to robustly choose relative important regressors whose marginal regression functions have significant effects on estimating the joint regression function. In the third step, based on these significant regressors that survive the screening procedure, a penalized composite quantile model averaging marginal regression is considered to further achieve sparse model weights and estimate the joint regression function. The sure independence screening property of the proposed screening procedure and sparse property of the penalized estimator are established under some regularity conditions. Numerical studies including both extensive simulation studies and an empirical application are considered to verify the merits of our proposed approach.