Abstract: For the high-dimensional quantile regression model with massive data, firstly, a subsampling algorithm based on the decorrelation score function was constructed to estimate the low-dimensional parameters of interest. Secondly, we derived the limit distribution of the proposed estimates and calculated the subsampling probability under the L-optimal criterion according to the asymptotic covariance matrix, giving an efficient two-step algorithm. The simulation and empirical analysis results show that the  optimal subsampling method is significantly superior to  the uniform subsampling method.

Key words: decorrelation score, high-dimensional, massive data, quantile regression, subsampling