  As computer resources become increasingly limited, traditional statistical
methods face challenges in analyzing massive data, especially in functional
data analysis. To address this issue, subsampling offers a viable solution by
significantly reducing computational requirements. This paper introduces a
subsampling technique for composite quantile regression, designed for efficient
application within the functional linear model on large datasets. We establish
the asymptotic distribution of the subsampling estimator and introduce an
optimal subsampling method based on the functional L-optimality criterion.
Results from simulation studies and the real data analysis consistently
demonstrate the superiority of the L-optimality criterion-based optimal
subsampling method over the uniform subsampling approach.
