Smoothing quantile regression for a distributed system

Quantile regression has become a popular alternative to least squares for providing comprehensive description of the response distribution, and robustness against heavy-tailed error distributions. However, nonsmooth quantile loss poses new challenges distributed estimation in both computation theoretical development. To address this challenge, we use convolution-type smoothing approach its Taylor expression transform nondifferentiable function into convex quadratic function, which admits fast scalable algorithm perform optimization under massive high-dimensional data. The proposed estimators are computationally communication efficient. Moreover, only gradient information is communicated at each iteration. Theoretically, show that, after certain number iterations, resulting estimator statistically as efficient global without any restriction on machines. Both simulations data analysis conducted illustrate finite sample performance methods.