Semiparametric Regression Analysis With Missing Response Data

Semiparametric regression model has been developed as an importantstatistics model since 1980s, it has been used widely in many fields, becuse thiskind of model concludes not only the parametric part, but also the nonpara-metric component, it also has stronger explanations. Theoretically, methodsof dealing with this model are more complicated than the pure parametric ornonparametric regression model.In practice, often not all variables may be available for various reasonssuch as unwillingness some sampled units supply the desired information, lossof information caused by uncontrollable factors, failure on the part of inves-tigator to gather correct information, and so on. Recently, statisticans paidmore attention for dealing with the problem about missing data.In this paper, we consider the partially linear model with random miss-ing response. In current literature, there are many methods to dealing withmissing data, such as complete-case, imputation, and so forth. Based on thecomplete-case, We constructe the empirical likelihood ratio confidence regionfor the parametric component in the partially linear model, which presenta new way to treat this model. Under quite general conditions, we provethe empirical likelihood ratio statistic is asymptotically chi-squre distribution.Therefore, the empirical likelihood ratio confidence region can be constructed accordingly. In addition, a simulation study is carried out to compare theproposed method with the normal approximation-based methods. It is shownthat, the confidence region constructed by empirical likelihood has higher con-verage accuracy and shorter interval lengths.