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Title: Incorporating graphical structure of predictors in sparse quantile regression Authors:  Wenlu Tang - The Chinese University of Hong Kong (China) [presenting]
Zhanfeng Wang - University of Science and Technology of China (China)
Yuanyuan Lin - The Chinese University of Hong Kong (Hong Kong)
Xiaohui Liu - Jiangxi University of Finance and Economics (China)
Abstract: Quantile regression in high dimensional settings is useful in analyzing high dimensional heterogeneous data. 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 (ADMM) 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 microarray dataset.