Part Of The Empirical Likelihood Under The Lack Of Response Variable Linear Ev Model In Statistical Inference

In fact, we often meet error-in-variable models in the real statistical studies, this kind of models is very important issues in the theory and application, especially in the determination of science, economics, social studies, linguistics, agriculture, epidemiology and so onc however, the response variables are missing, which are also frequently encountered in practical applications, such as inclinical diagnosis, public opinion polls market survey, socio-economic research and many observational studies.therefore, study the response variables which are missing in part of the linear EV models have high practical value.Empirical likelihood is a nonparametric method of inference based on a data-driven likelihood ratio function. Like the bootstrap,The essence of the method is maximizing nonparametric likelihood ratio under some restrictions, so that the relationship between the interested parameters and the likelihood ratio is constructed. What is more, The empirical likelihood ratio has a limiting chi-squared distribution, It can make to estimate and hypothesis test. What is more, empirical likelihood need not to estimate the covariance matrix, which is often hard to estimated.In this thesis, a partially linear error-in-variable models with missing response data is considered, we are interest in inference for regression coefficient and baseline function. A bias-corrected technique is used to construct the empirical likelihood ratio statistic.under some suitable condition, It is proved that the proposed statistic is asymptotically standard chi-square distribution by this result we construct the confidence region of the parameter. Also, a class of estimators for parameter of interest is proposed their asymptotic distribution is obtained. At last A simulation study is undertaken to compare the empirical likelihood with the normal approximation-based method in terms of coverage accuracies and average lengths of confidence region.