THE L1-PENALIZED QUANTILE REGRESSION FOR TRADITIONAL CHINESE MEDICINE SYNDROME MANIFESTATION

Traditional Chinese medicine syndrome manifestation is a nonlinear complex system, which has attracted much attention on its role in clinical study. With the help of the modern technique of the big data analysis, in this paper we provide a high-dimensional quantile regression model for Traditional Chinese medicine syndrome manifestation, where the term "high-dimensional" means that the number of observations is much less than the number of covariates. Moreover, we assume that the unknown vector is sparse, so we propose the use of an L-1-penalized quantile regression estimator to solve the model. Our estimator does not need any knowledge of of standard deviation of the noises or any moment assumptions of the noises. We show that the L-1-penalized quantile regression estimator (QRE) possesses near oracle performance, i.e. with large probability, the L-2 norm of the estimation error is of order O(root s(log p)/n). The result is true for a wide range of noise distributions, even for the Cauchy distribution. In addition, we apply an alternating direction method to find the L-1-penalized QRE, which possesses the global convergence. Numerical results are reported to demonstrate the efficacy of our proposed method.