| In traditional statistical analysis,the influence of covariates with errors is usually neglected to study models.However,when measurement errors exist,both linear and nonlinear models are assumed to be specific forms with some unknown parameters.Because of the inflexibility of these parameter models in calculation and the bias in estimation,this makes the nonparametric measurement error model popular.Many existing methods are developed under the assumption of known measurement error distribution and unknown true covariant distribution,and based on the famous N-W kernel estimation,the local constant estimation of regression function is established by using deconvolution kernel.However,due to the inherent defects of kernel estimation such as marginal effect,it is difficult to further improve the estimation accuracy.Many methods have been adopted to improve the research effect of measurement error model based on kernel estimation.Based on this point,this paper proposes an estimation method based on Bernstein polynomial type model.Firstly,this paper introduces the research status of kernel estimation method and measurement error model,and summarizes the shortcomings of existing research.Secondly,the Bernstein type polynomial estimation of measurement error model is proposed in this paper,and the consistency of the estimation is given.Finally,numerical simulation shows that the method proposed in this paper is superior to the estimation method based on the measurement error model of kernel estimation,which shows the effectiveness of the method. |
