Estimations Of Partially Linear Varyingcoefficient Model Witn Measurement Error Under Constraint Conditions

As one of the semi-parametric regression models,the partially linear varyingcoefficient model combines the advantages of linear regression models and the nonparametric models.This model can be applicated wider range and fitted more effective.The measurement error model is closer to the actual research situation because it considers the measurement error caused by factors such as the environment,measurement tools and weather that are unavoidable in actual research.At the same time,some preset conditions or assumptions in actual research will make the parameters in the model with constraints.The purpose of this paper is to study the estimation and asymptotic properties of estimators for partially linear varying-coefficient model with measurement errors under constraints.In Chapter 3,the corrective estimator of the model is obtained by using the local correction estimation method and the profile least squares method and then combined with the Lagrange multiplier method to carry out the partially linear varying-coefficient model with the measurement error of the nonparametric part of the covariate under the constraint condition.Estimate get the constrained estimator of the parameters and function coefficients.At the same time,the asymptotic properties of estimators are proposed and proved under appropriate conditions.Finally,the data simulation is carried out by R software to study the performance of the estimated estimator proposed in this paper under the limited sample size.On the basis of Chapter 3,the estimation problem of the partially linear varyingcoefficient model in which the parameters and the nonparametric part of the covariates contain measurement errors under the condition of random constraints is studied.The bias-corrected random constraint estimators of parameters and function coefficients are obtained by the bias-corrected profile hybrid estimation method and the asymptotic properties of parameter estimators and function coefficients are further deduced.Finally,the data simulation research is carried out by R software and it is verified that although the asymptotic properties of the bias-correcting estimator without considering the random constraints are the same as the asymptotic properties of the bias-correcting mixed estimators considering the random constraints,but with a limited sample size the performance below is not the same.