Weighted local linear CQR for varying-coefficient models with missing covariates

Robust and sparse learning of varying coefficient models with high-dimensional features

Varying coefficient model (VCM) is extensively used in various scientific fields due to its capability of capturing the changing structure of predictors. Classical mean regression analysis is often complicated in the existence of skewed, heterogeneous and heavy-tailed data. For this purpose, this work employs the idea of model averaging and introduces a novel comprehensive approach by incorporating quantile-adaptive weights across different quantile levels to further improve both least square (LS) and quantile regression (QR) methods. The proposed procedure that adaptively takes advantage of the heterogeneous and sparse nature of input data can gain more efficiency and be well adapted to extreme event case and high-dimensional setting. Motivated by its nice properties, we develop several robust methods to reveal the dynamic close-to-truth structure for VCM and consistently uncover the zero and nonzero patterns in high-dimensional scientific discoveries. We provide a new iterative algorithm that is proven to be asymptotic consistent and can attain the optimal nonparametric convergence rate given regular conditions. These introduced procedures are highlighted with extensive simulation examples and several real data analyses to further show their stronger predictive power compared with LS, composite quantile regression (CQR) and QR methods.

DGQR estimation for interval censored quantile regression with varying-coefficient models

This paper propose a direct generalization quantile regression estimation method (DGQR estimation) for quantile regression with varying-coefficient models with interval censored data, which is a direct generalization for complete observed data. The consistency and asymptotic normality properties of the estimators are obtained. The proposed method has the advantage that does not require the censoring vectors to be identically distributed. The effectiveness of the method is verified by some simulation studies and a real data example.