Semi-Parametric Estimation Method Based On Bernstein Method

The semi-parametric model is a statistical model that was developed in the1980 s.It has now become one of the important statistical models in statistics.It has both the advantages of the parametric model and the non-parametric model,the model contains both parameters part and non-parametric part,its more powerful adaptability and flexibility as well as the advantage of being more in line with the real situation in applications,have received a lot of attention from scholars in the past two decades.The semiparametric regression model is one of the research hotspots of semiparametric statistics,and the two-stage estimation method is one of the commonly used methods of semiparametric regression estimation.This paper uses the Bernstein polynomial model to improve the two-stage estimation method.First,this paper reviews the research history and current status of semiparametric problems,and introduces the Bernstein-type polynomial estimation method.Second,the Bernstein estimation is used in two-stage estimation to replace the kernel estimation,which proves that the improved estimation is consistent;finally,numerical experiments were conducted on different semiparametric models.The results illustrate the effectiveness of the method and point out that the method is superior to the original two-stage estimation.