A propensity score adjustment method for regression models with nonignorable missing covariates

In a linear regression model with nonignorable missing covariates, non-normal errors or outliers can lead to badly biased and misleading results with standard parameter estimation methods built on either least squares- or likelihood-based methods. A propensity score method with a robust and efficient regression procedure called composite quantile regression for parameter estimation of the linear regression model with nonignorable missing covariates is proposed. Semiparametric estimation of the propensity score is based on the exponentially tilted likelihood approach. Asymptotic properties of the proposed estimators are systematically investigated. The proposed method is resistant to heavy-tailed errors or outliers in the response. Simulation studies and real data applications are used to illustrate its potential impacts and benefits compared with conventional methods.