🤖 AI Summary
This study addresses the high computational cost of quantile regression for large-scale longitudinal data by proposing an efficient estimation method based on optimal Poisson subsampling. For the first time, optimal Poisson subsampling is integrated into the longitudinal quantile regression framework, combined with a weighted smoothed quantile generalized estimating equation and regularization techniques to achieve sparse parameter estimation. The authors establish the corresponding asymptotic theory to support the proposed approach. Numerical experiments and real data analysis demonstrate that the method significantly outperforms uniform Poisson subsampling in both estimation accuracy and computational efficiency, while the regularized estimator exhibits strong variable selection performance.
📝 Abstract
To address the computational challenges arising from large-scale longitudinal data, an optimal Poisson subsampling algorithm is proposed for quantile regression. The proposed method can substantially alleviate computational burden. Under some regularity conditions, we derive the asymptotic properties of the estimators from weighted quantile generalized estimating equations. For practical implementation, an efficient algorithm is proposed for parameter estimation. Furthermore, asymptotic theory is established for penalized weighted smooth quantile generalized estimating equations, and regularized parameter estimation is performed within the optimal Poisson subsampling framework. Both numerical simulations and a real data application demonstrate that the proposed optimal Poisson subsampling algorithm outperforms the uniform Poisson subsampling algorithm, and the regularized estimation exhibits satisfactory performance as well.