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.

翻译：随着计算资源日益受限，传统统计方法在分析大规模数据时面临挑战，尤其是在函数型数据分析领域。为解决这一问题，子抽样通过显著降低计算需求提供了一种可行的解决方案。本文针对大规模数据集中的函数型线性模型，提出了一种复合分位数回归的子抽样技术。我们建立了子抽样估计量的渐近分布，并基于函数型L最优性准则提出了一种最优子抽样方法。模拟研究和实际数据分析结果一致表明，基于L最优性准则的最优子抽样方法优于均匀子抽样方法。