A new relative error estimation for partially linear multiplicative model

Abstract

In this paper, a new product relative error estimation method for the partially linear multiplicative regression model (PLMM) is proposed. Both parametric and nonparametric parts are estimated by the least product relative error (LPRE) criterion and local smoothing technique. Besides, regularization conditions are given to establish the consistent and asymptotic normal properties. Finally, several numerical simulations and a real data analysis are included to show the performance of the proposed approach.

Keywords:

• Asymptotic normality
• Least product relative error
• Multiplicative model
• Partially linear model

Additional information

Funding

This work is partly supported by National Natural Science Foundation of China (Grant No. 11761020), Science and Technology Foundation of Guizhou Province (Grant No. QKHZK[2021]YB011) and Training Foundation of Guizhou University (Grant No. GZUPY[2019]62).