论文标题
功能分位数回归的最佳子采样
Optimal subsampling for functional quantile regression
论文作者
论文摘要
亚采样是处理大量数据的有效方法。在本文中，我们研究了协变量是函数时线性分位回归的最佳亚采样。首先得出亚采样估计量的渐近分布。然后，我们基于A型标准获得了最佳的子采样概率。此外，还提出了鉴于协变量的响应变量的密度，也提出了修改后的子采样概率，而在实践中也更容易实施。关于合成和真实数据的数值实验表明，所提出的方法始终优于均匀采样的方法，并且可以基于完整数据良好的计算工作效果近似结果。
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.
