In this paper,the varying-coefficient partially linear regression model considering the measurement error,that is,the estimation problem of the semi-variable coefficient EV model is studied.In the paper,the form of the variable coefficient model,the commonly used estimation method and the least squares cross-validation bandwidth selection method are given.On this basis,for the model considering the measurement error,this paper gives a least squares estimation method with correction based on the local polynomial method.A concrete expression of the constant coefficient and the function coefficient under the measurement error is given.When the error variance of the measurement error is unknown,this paper also gives an estimation method of the unknown variance,that is,using the repeated observations of the same variable for estimation.After that,a generalized likelihood ratio test for the function parameters is also proposed to verify that the data is suitable for this model.In order to evaluate the performance of the parameter estimation method and test program proposed in this paper,the paper conducted two computer simulation experiments and a practice of real data based on heart disease research in the third chapter.The results show that the choice of bandwidth will affect the function.The fitting effect of the coefficient,and the estimation effect of the semi-variable coefficient EV model studied in this paper is better than that of ignoring the measurement error.When the sample size increases,the former's estimation effect is closer to the effect of true value.The former's estimation effect is also closer to the effect of no-measure error model.This result indicates that the results of the paper can be used for asymptotically effective statistical inference of some models.At the same time,the model has a good application prospect in the field of medical research.The focus of this paper is on the case where linear covariates have additive measurement errors,while the function coefficients are not measured.Therefore,the case where the measurement error is not an additive error and the case where the variable coefficient part also has a measurement error can be further studied.In this case,the varyingcoefficient partially linear regression model can solve more practical problems. |