Estimation Of Nonlinear Regression Models With Measurement Error

Parametric regression model,as an important type of regression model,lays the foundation for the study of non-parametric and semi-parametric models with gradually diversified and generalized structures,and therefore plays a vital role in the field of model research.Nonlinear models belong to parametric regression models.Due to the advantages such as known functional forms,abundant theories and methods,nonlinear models are widely applied in different fields.However,the collected data is unavoidable to be affected and interfered by various aspects such as the external environment,the structure of the measuring instrument,and the technical level of the surveyor,resulting in measurement errors in almost all application areas.Ignoring these measurement errors will lead to inconsistent estimators with asymptotic bias.Therefore,the research motivation of the paper is to obtain asymptotically unbiased and consistent effective estimators of unknown parameters in the nonlinear measurement error models.This paper studies the parameter estimation problem of nonlinear measurement error models in univariate and multivariate situations.First,the estimator in this paper is based on the approximate maximum quasi-likelihood estimator proposed by Hsiao et al.(1997)^[27].But unlike Hsiao et al.(1997)^[27]assuming the conditional expectation and variance functions of the real covariate with respect to the proxy variable are known,the paper innovatively introduces non-parametric local regression estimators of unknown functions.Based on univariate local polynomial regression and multivariate kernel regression,a modified approximate maximum quasi-likelihood estimate is obtained.Then,under reasonable assumptions,this paper proves the consistency and asymptotic normality of the corresponding estimators.Finally,in order to further illustrate the advantages of the modified estimators,the 3th and 4th chapters utilize numerical simulation examples and actual data of monozygotic twins for analysis,and visually show the robustness of the modified estimators,as well as higher precision and accuracy.