A penalized least product relative error loss function based on wavelet decomposition for non-parametric multiplicative additive models

• Published in: Journal of computational and applied mathematics Vol. 432; p. 115299
• Main Authors: Yang, Fan, Li, Zhanyang, Xue, Yushan, Yang, Yuehan
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01-11-2023
• Subjects: Least product relative error; Non-parametric multiplicative additive models; SCAD; Wavelet decomposition; Non-parametric multiplicative additive models; Least product relative error; SCAD; Wavelet decomposition
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2023.115299

In this paper, an estimation method based on wavelet decomposition is proposed for non-parametric multiplicative additive models. The proposed method can transform the estimation problem of non-parametric models into the estimation of parametric models without assuming the error distribution. To achieve the sparsity of the model, we apply the smoothly clipped absolute deviation (SCAD) penalty to estimate and select the variables based on the least product relative error loss function. Simulation results support the theoretical characteristics. We show that the proposed method is more effective than the traditional spline estimation method. Applications further show the performance of the proposed method with the actual data.