Incorporating Graphical Structure of Predictors in Sparse Quantile Regression
提出一种利用预测变量间图形结构改进稀疏分位数回归的方法，在参数估计、模型选择和预测上优于现有方法，并证明了模型选择一致性和oracle性质。
Quantile regression in high-dimensional settings is useful in analyzing high-dimensional heterogeneous data. In this article, different from existing methods in quantile regression which treat all the predictors equally with the same priori, we take advantage of the graphical structure among predictors to improve the performance of parameter estimation, model selection, and prediction in sparse quantile regression. It is shown under mild conditions that the proposed method enjoys the model selection consistency and the oracle properties. An alternating direction method of multipliers algorithm with a linearization technique is proposed to implement the proposed method numerically, and its convergence is justified. Simulation studies are conducted, showing that the proposed method is superior to existing methods in terms of estimation accuracy and predictive power. The proposed method is also applied to a real dataset.