In this paper, we study the functional linear multiplicative model based on the least product relative error criterion. Under some regularization conditions, we establish the consistency and asymptotic normality of the estimator. Further, we investigate the optimal subsampling for this model with massive data. Both the consistency and the asymptotic distribution of the subsampling estimator are first derived. Then, we obtain the optimal subsampling probabilities based on the A-optimality criterion. Moreover, the useful alternative subsampling probabilities without computing the inverse of the Hessian matrix are also proposed, which are easier to implement in practise. Finally, numerical studies and real data analysis are done to evaluate the performance of the proposed approaches.

翻译：在本文中,我们根据最低产品相对误差标准研究功能线性线性多复制模型。在某些正规化条件下,我们确定估计值的一致性和无症状常态性。此外,我们用大量数据调查这一模型的最佳子抽样,首先得出子抽样估计值的一致性和无症状分布。然后,我们根据A-最佳性标准获得最佳子抽样概率。此外,还提出了不计算赫西安矩阵反差的有用的次级抽样,这在实际中比较容易执行。最后,进行了数字研究和实际数据分析,以评估拟议方法的绩效。