Unified Approach to Partially Linear Model and Cox Proportional Hazards Model with Missing Covariates
In regression analysis the problem of missing covariate data is common in various fields of application. Many methods have been developed to deal with this problem in the past three decades. These methods are workable under most missing data scenarios. However, when missing covariate data appear in a general missing data pattern, many methods become too complicated in computation. In this thesis, we extend the unified approach of Chen and Chen (2000) and Zhao et al. (2013) to deal with partially linear model (Engle et al., 1986) and Cox proportional hazards model (Cox, 1972) with missing covariates. The unified approach possesses some superior characteristics in dealing with regression models with missing data. First, the unified approach requires less extra assumptions to be applied than many other methods, which may need additional modeling for variables with missing values. Second, this extension of the unified approach can deal with both the simple monotone missing data pattern and the general missing data pattern under missing completely at random and missing at random settings. Third, no iteration is needed in computing the proposed estimate. In general, compared to other methods, the unified approach is conceptually and computationally simple. This thesis describes the proposed estimators separately for the partially linear model and the Cox proportional hazards model with missing covariates. The asymptotic properties of the estimators are investigated or justified. Simulations are conducted under different settings to examine the performance of the proposed estimators for these two models.