Least product relative error estimation for functional multiplicative model and optimal subsampling

TL;DR

This paper introduces a novel least product relative error estimation method for functional multiplicative models, establishing its statistical properties and optimizing subsampling strategies for large datasets.

Contribution

It develops a new estimation approach based on least product relative error, proves its consistency and asymptotic normality, and proposes practical optimal subsampling methods.

Findings

Estimator is consistent and asymptotically normal.

Optimal subsampling probabilities improve computational efficiency.

Numerical studies validate the proposed methods.

Abstract

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.