Least product relative error estimation for identification in multiplicative additive models

In this paper, we study the multiplicative additive models based on the least product relative error (LPRE) criterion proposed by Chen et al. (2016). We adopt the B-spline basis functions to estimate the nonparametric functions. The SCAD penalty function is used to identify the linear and zero components in the models. Furthermore, we prove the optimal convergence rate of the nonparametric function estimation and the variable selection consistency. Finally, the simulation results and case analysis demonstrate that the performance of the proposed method outperforms the state-of-the-art baseline methods. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

This study examines the multiplicative additive models based on the LPRE criterion proposed by Chen et al. (2016), utilizing B-spline basis functions for nonparametric function estimation and SCAD penalty function for variable selection. The research demonstrates optimal convergence rate and variable selection consistency, with simulation results and case analysis showing superior performance compared to existing methods.