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

Abstract

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.