Distributed smoothed rank regression with heterogeneous errors for massive data

Rank estimation methods are robust and highly efficient for estimating linear regression model. This paper investigates the rank regression estimation for massive data. To deal with the situation that the data are distributed heterogeneously in different blocks, we propose a weighted distributed rank-based estimator for massive data, which can improve the efficiency of the standard divide and conquer estimator. Under mild conditions, the asymptotic distributions of the weighted distributed rank-based estimator is derived. To achieve sparsity with high-dimensional covariates, the variable selection procedure is also proposed. Both simulations and data analysis are included to illustrate the finite sample performance of the proposed methods.