Distributed Estimation for ℓ0-Constrained Quantile Regression Using Iterative Hard Thresholding

Distributed frameworks for statistical estimation and inference have become a critical toolkit for analyzing massive data efficiently. In this paper, we present distributed estimation for high-dimensional quantile regression with ℓ0 constraint using iterative hard thresholding (IHT). We propose a communication-efficient distributed estimator which is linearly convergent to the true parameter up to the statistical precision of the model, despite the fact that the check loss minimization problem with an ℓ0 constraint is neither strongly smooth nor convex. The distributed estimator we develop can achieve the same convergence rate as the estimator based on the whole data set under suitable assumptions. In our simulations, we illustrate the convergence of the estimators under different settings and also demonstrate the accuracy of nonzero parameter identification.