Multiply Robust Estimation In Partially Linear Model With Missing Data

Missing data is an ubiquitous problem in actual life, which is also a very important re-search subject in statistical analysis. There are many statistical methods to deal with Missing data, and doubly robust estimators are widely used among them since they provide double pro-tection on estimation consistency against model misspecifications. However, they allow only a single model for the missingness mechanism and a single model for the data distribution, and the assumption that one of these two models is correctly specified is restrictive in practice. Recently, methods of multiply robust estimators have been considered, one of them is allowing multiple models for both the missingness mechanism and the data distribution, and the estimator is con-sistent if any one of those models is correctly modeled. As the partially linear model is a kind of semiparametric model which is widely used in practical application, we apply this approach to estimate the parameter of the partially linear model with the response variable missing at ran-dom, and the asymptotic properties are established. At last, we show the merits of the estimator by our simulation results and analyse the data collected from the AIDS Clinical Trials Group Protocol 175.The contents of the paper are as follows. In section 1, we introduce some basic models and basic knowledge involved in this paper. In section 2, We describes the robust estimation procedure, and the asymptotic properties are established. In section 3, the finite sample perfor-mance of our method is investigated. In section 4, a real dataset is demonstrated by applying our approach. All the technical proofs of the main results are deferred to section 5. We end the paper with a brief discussion in Section 6.