Least product relative error estimation for identification in multiplicative additive models

Abstract

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.