Abstract
Traditional statistical analysis is challenged by modern massive data sets, which have huge sample size and dimension. Quantile regression has become a popular alternative to least squares method for providing comprehensive description of the response distribution and robustness against heavy-tailed error distributions. On the other hand, non-smooth quantile loss poses a new challenge to massive data sets. To address the problem, we transform the non-differentiable quantile loss function into a convex quadratic loss function based on Expectation-maximization (EM) algorithm using an asymmetric Laplace distribution. Both simulations and real data application are conducted to illustrate the performance of the proposed methods.
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