Quantile regression for massive data set

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.

Keywords:

• Asymmetric Laplace distribution
• EM algorithm
• Massive data
• Quantile regression

Additional information

Funding

We would like to acknowledge support for this project from the Ministry of Education of the People’s Republic of China, Humanities and Social Science Foundation (No. 22YJC910005).