This paper investigates distributed Composite Quantile Regression (CQR) estimation for high-dimensional linear regression models, presenting a robust and computationally efficient approach. Methodologically, each iteration requires only the master machine to solve a shifted \(\varvec{\ell }_{\varvec{1}}\) -regularized least squares problem, leveraging a newly established theoretical link between composite quantile regression loss and squared loss functions. The proposed estimator achieves asymptotic equivalence to the full-data estimator after a finite number of iterations, with identical convergence properties. Empirical evaluations through simulations and real-data analyses demonstrate the method’s strong finite-sample performance, validating its practical applicability and statistical efficiency in distributed computing environments.
