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.

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