Research On Two-step Estimation Of Semiparametric Model Based On Bernstein Polynomials

Semi-parametric statistics is one of the important branches of statistics.The model includes both parametric and non parametric parts,which makes the model flexible and can better fit the real data.Semi-parametric regression model is one of the research hotspots of semi-parametric statistics,and the two-step estimation method is one of the common methods of semi-parametric regression estimation.In this paper,Bernstein polynomial model is used to improve the original twostep estimation method.Firstly,this paper reviews the history and current situation of semi parametric model,and introduces Bernstein Type polynomial estimation method;Secondly,Bernstein's method is used to estimate the nonparametric part of the two-step estimator,which replaces the original kernel estimator and proves the consistency of the improved estimator;Finally,numerical experiments are carried out for different semiparametric models.The results show that the method is effective and better than the original two-step estimation.