Non-parametric Estimation Method Based On Bernstein Method

Nonparametric statistics is one of the important branches of statistics,and nonparametric regression is an important research direction in nonparametric s-tatistics.The basic idea of nonparametric regression is to represent the function to be estimated as a conditional expectation,and to obtain an estimate of the final function by estimating the joint distribution density and the marginal distribution density.This paper uses Bernstein-type polynomial estimation methods to study nonparametric regression problems.First,the paper reviews the development his-tory and research status of nonparametric statistics and nonparametric regression,and introduces the research history and current status of traditional density esti-mation methods such as kernel methods;Secondly,the Bernstein type polynomial density estimation method is introduced,and the Bernstein solution method for non-parametric regression problems is given,which shows that the obtained estimates are consistent;Finally,the effectiveness of the method is given through simulation studies of different functions,and the comparison with traditional kernel methods shows that the proposed method is superior to the kernel method.