Block average quantile regression for massive dataset

Abstract

Nowadays, researchers are frequently confronted with challenges from large-scale data computing. Quantile regression on massive dataset is challenging due to the limitations of computer primary memory. Our proposed block average quantile regression provides a simple and efficient way to implement quantile regression on massive dataset. The major novelty of this method is splitting the entire data into a few blocks, applying the convectional quantile regression onto the data within each block, and deriving final results through aggregating these quantile regression results via simple average approach. While our approach can significantly reduce the storage volume needed for estimation, the resulting estimator is theoretically as efficient as the traditional quantile regression on entire dataset. On the statistical side, asymptotic properties of the resulting estimator are investigated. We verify and illustrate our proposed method via extensive Monte Carlo simulation studies as well as a real-world application.