Statistical Inference For Partially Linear Varyingcoefficient EV Models With Missing Responses

In this paper,we mainly consider the statistical inference for partially linear varying coefficient errors in variables models in the nonparametric part and the responses are missing at random.The paper is divided into two parts.In the first part,Under the conditions of measurement error in the nonparametric part and missing responses at random,we investigate the estimation of both parametric and nonparametric components.in order to facilitate the processing of missing data,our estimator is constructed by using complete-case observations only.then,based on local linear smoothing techniques,profile least-squares and bias-corrected methods,we obtained estimators successfully about both parametric and nonparametric components.And the resulting estimator are shown to be asymptotically normal.Besides,we construct two types of estimators for missing responses,and prove the asymptotic normality of estimators.A simulation study is conducted to illustrate the finite sample performance of the proposed method.In the second part,we construct the confidence regions of parametric components for partially linear varying coefficient under the same conditions.To avoid to estimate the asymptotic covariance in establishing confidence region of the parametric component with the normal-approximation method,we define an empirical likelihood based statistic and show that its limiting distribution is chi-squared distribution.Then,the confidence regions of the parametric component with asymptotically correct coverage probabilities can be constructed by the result.The simulation results shows that the empirical likelihood method has better finite sample properties compared with the normal approximation method.Finally,Boston housing data is analyzed for illustration.