Optimal subsampling for composite quantile regression model in massive data

The composite quantile regression (CQR) estimator is a robust and efficient alternative to the ordinary least squares estimator and single quantile regression estimator in linear models. For massive data, two different optimal subsampling probabilities through minimizing the trace of the asymptotic variance–covariance matrix for a linearly transformed parameter estimator and the asymptotic mean squared error of the resultant estimator are proposed to downsize the data volume and reduce the computational burden. Furthermore, to improve the efficiency of the ordinary CQR, the optimal subsampling for the weighted CQR estimator is also studied. We also propose iterative subsampling procedures based on two optimal subsampling probabilities to estimate the variance–covariance matrix. The finite-sample performance of the proposed estimators is studied through simulations and an application to household electric power consumption data is also presented.