Quantile Regression of Ultra-high Dimensional Partially Linear Varying-coefficient Model with Missing Observations

In this paper, we focus on the partially linear varying-coefficient quantile regression with missing observations under ultra-high dimension, where the missing observations include either responses or covariates or the responses and part of the covariates are missing at random, and the ultra-high dimension implies that the dimension of parameter is much larger than sample size. Based on the B-spline method for the varying coefficient functions, we study the consistency of the oracle estimator which is obtained only using active covariates whose coefficients are nonzero. At the same time, we discuss the asymptotic normality of the oracle estimator for the linear parameter. Note that the active covariates are unknown in practice, non-convex penalized estimator is investigated for simultaneous variable selection and estimation, whose oracle property is also established. Finite sample behavior of the proposed methods is investigated via simulations and real data analysis.