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 compo...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2022-04, Vol.404, p.113886, Article 113886
Main Authors: Ming, Hao, Liu, Huilan, Yang, Hu
Format: Article
Language:English
Subjects:
B-spline
Least product relative error
Model selection
Multiplicative partially linear additive models
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Summary: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.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2021.113886