  Subsampling is an efficient method to deal with massive data. In this paper,
we investigate the optimal subsampling for linear quantile regression when the
covariates are functions. The asymptotic distribution of the subsampling
estimator is first derived. Then, we obtain the optimal subsampling
probabilities based on the A-optimality criterion. Furthermore, the modified
subsampling probabilities without estimating the densities of the response
variables given the covariates are also proposed, which are easier to implement
in practise. Numerical experiments on synthetic and real data show that the
proposed methods always outperform the one with uniform sampling and can
approximate the results based on full data well with less computational
efforts.
