Bernstein Polynomial Estimation Of Additive Model

Statistical inference of nonparametric regression model has become an important field of statistical research.As a common multivariate nonparametric regression model,additive model is very useful in dealing with practical problems.Recently,the nonparametric estimation of additive model has also become the center of model research.There are many estimation methods of additive models that have been proposed,such as classical Backfitting iterative algorithm,smoothing Backfitting iterative algorithm,marginal integral method,spline fitting method and two-stage estimation method.These methods are based on kernel method to estimate the additive component function of additive model.However,the boundary effect and high calculation cost of kernel method lead to limited improvement of estimation effect.Therefore,this paper proposes the Bernstein method,which is used to study the estimation of the additive component function of the additive model.Firstly,this paper reviews the research background and research status of nonparametric additive models and Bernstein polynomials at home and abroad,gives the form of nonparametric additive models,introduces in detail the specific process of estimating the additive component function using kernel estimation method,introduces the univariate and multivariate Bernstein polynomial estimation methods,and points out the excellent properties of Bernstein polynomial estimation methods.Secondly,for the general additive model and the additive model with interactive terms,this paper gives the Bernstein type polynomial estimation method of the additive component function,and shows that the estimators are consistent.Finally,six different forms of additive component functions are selected for simulation research,and the simulation effect is judged according to the integral mean square error.The simulation results show the effectiveness of the method proposed in this paper,and it is better than the traditional method based on kernel estimation.