Distributed inference for the quantile regression model based on the random weighted bootstrap

The adoption of quantile regression has become increasingly prevalent because of its robustness and comprehensiveness compared to the ordinary least squares approach. However, in analyzing distributed data, it is challenging to estimate the unknown parameter and construct its confidence interval, while the existing related method suffers from coverage distortion at tail quantiles with levels close to 0 or 1, caused by the nuisance parameter estimation. This paper proposes a novel distributed statistical inference method for the quantile regression model by incorporating the random weighted bootstrap method to circumvent the nuisance parameter estimation problem. A modified random weighted bootstrap is also developed to suit the case when the number of machines is relatively small. The new methods are communication efficient and have reasonable finite sample performance at tail quantiles. Theoretical properties are established. Simulations and real data analysis are also devoted to verifying the theoretical properties and illustrating the finite sample performance.