Estimation For Modal Linear Model With Error In Variables

Modal linear regression model is a simple and commonly used statistical model in statistical research.Compared with mean regression and quantile regression,modal regression estimation not only has good robustness and higher inference efficiency for asymmetric error distribution or abnormal data,but also the obtained estimation hardly loses efficiency under normal error.When the covariates have measurement errors,the parameter estimation of modal linear regression model is a very important research topic at present.The main results of this thesis are the following two parts.1.When the measurement error obeys multivariate Laplace distribution,a robust estimation of the modal linear regression coefficient is obtained.Considering that covariates cannot be directly observed,we construct a new kernel estimation by deconvolving kernel method,and then obtain the estimation of parameters.Under certain regular conditions,the consistency and convergence rate of the estimators are derived,and the asymptotic normality of the proposed estimators is proved.Monte-Carlo simulation shows that the method proposed in this paper performs well under limited samples.2.When the measurement error obeys the general smooth distribution that the tail of the characteristic function decays to zero in polynomial form,the parameter estimation is obtained by deconvolving kernel method.Given some mild assumptions,the large sample properties of the proposed method are established.Numerical experiments further verify the robustness and effectiveness of the proposed method.