| Semi-parametric additive model method is a statistical fitting method,which has been applied in many fields.Nowadays,semi-parametric additive model has attracted the attention of statisticians and become a very important statistical model.Semi-parametric additive model contains parametric linear components and nonparametric additive components.Because it includes the advantages of both parametric and nonparametric models,semi-parametric additive model is more flexible than conventional linear models.Compared with the general nonparametric regression model,it is more eective and avoids the dimension disaster.In addition,the model has strong adaptability and flexibility,and in data research,the semi-parametric additive model is more in line with the actual situation.This paper mainly studies the estimation of semi-parametric additive model.Based on the classical two-stage estimation strategy,this paper adopts Bernstein polynomial estimation method in the estimation of nonparametric additive component function,thus improving the two-stage estimation strategy and further studying the Bernstein polynomial estimation of semi-parametric additive model.Firstly,this paper introduces the research background and present situation of semiparametric additive model.Secondly,the Bernstein polynomial density estimation method is introduced.In the two-stage estimation strategy,the kernel estimation is replaced by Bernstein polynomial estimation,and the additive component function estimation is obtained,which proves the consistency of the estimation.Finally,numerical studies on dierent models show the eectiveness of the proposed method,which is obviously superior to the two-stage estimation based on kernel method in estimation accuracy. |
