Empirical Likelihood Inference For The Parameter Of A Linear Error-variable Models With Missing Response

In the study of many practical problems, such as:polls, sampling survey, survival analysis medical statistics, biological research, etc. Various reason, could produce a large amount of data missing, the reason, the study of regression model in the case of missing data is still a hot topic in the current statistics. EV(errors-in-variables) model is also called the measurement error model, that is regression models with the independent variable and dependent variable error. However, the data are often obtained with measurement error in real life. Therefore, studying the EV model of missing data more matches the actual circumstances and have practical value.One new complement method is used.In this paper. The missing response problem in the EV models is investigated. The missing meet MAR(missing at random) missing mechanism. On the one hand, the confi-dence interval of the parameter are estimated by using four method. Respectively, based on the observation data completely, based on weighted, based on the inverse probabili-ty weighted method, normal approximation method. On the other hand, the confidence interval of the mean are estimated by using four method, respectively, Linear regres-sion complement method, based on weighted, based on the inverse probability weighted method, normal approximation method. Finally, the confidence interval and the average coverage of the interest parameter have simulated by the Matlab software. Simulation results show empirical likelihood method is better than other methods in terms of cover-age probabilities and the average lengths of confidence region. Using inverse probability weighted method have high coverage and shorter length than other three methods. The confidence region of the parameter by using this method don’t need to be adjusted. Thus this new method improves the precision of parameter estimation.The innovation of this paper is:talking about the structure of the linear EV models for the parameter β at missing data. It is proved that the constructed empirical log-likelihood statistic for the parameter β is asymptotically standard chi-square distribution. The confidence interval of the parameter β are estimated by using four method; At the same time, we construct empirical log-likelihood ratio statistics for the parameter θ by using inverse probability weighted method. It is proved that the constructed empirical log-likelihood statistic for the parameter θ is asymptotically standard chi-square distribution. The confidence interval of the parameter θ are estimated by using this method; Three others were used respectively to construct confidence regions of parameters beta and theta, Numerical simulation shows that the inverse probability weighted method is better than other methods.