Statistical Inference For Partially Nonlinear Varying-coefficient Models With Measurement Errors

The regression model occupies an important place in statistical models,its the-oretical research is rich and its application is more widely.As an important branch of the regression model,semiparametric models have been popular for combining ad-vantages of the parametric models and the nonparametric models.The model contains the parametric component and the nonparametric function to excavate the relevant information in the data.This practice greatly optimizes the fitting effect of the mod-el.As one of the semiparametric model,varying coefficient partially nonlinear model inherits the characteristics of the semiparametric model,and it reduces model's devia-tion and avoids the problem of 'curse of dimensionality' simultaneously.These features make the model more widely applied in practical problems.But in solving practical problems,often due to various reasons,the data cannot be accurately observed.For example,the tool or the non-standard operation in the process of measurement,the external environment influence,sampling and so on.In statistic study,the problem with measuring error is called 'measurement error problem' and the statistical models with measuring error is called 'errors-in-variables model'.In this paper,we mainly consider the partially nonlinear varying coefficient models with measurement errors,and the measurement errors are present in nonparametric part.We divide the errors into two categories,additive errors and nonadditive er-rors.We apply corrected profile least-squared to obtain the estimations of parameter and nonparametric part of the partially nonlinear varying coefficient models with addi-tive measuring errors,we also propose the GLR test to verify the coefficient functions is a constant vector or not.Under some conditions,we prove the asymptotic property of the results.For nonadditive measurement errors,we introduce two methods,corrected local polynomial procedure based on the optimal differential sequence and corrected unified procedure.Under appropriate assumptions,we give the asymptotic inference properties of the estimations of the two methods.Finally,numerical simulation and practical examples are given to verify the validity of the proposed estimation method and test method.