Projection-based Consistent Test for Linear Regression Model with Missing Response and Covariates

In recent years, there has been a large amount of literature on missing data. Most of them focus on situations where there is only missingness in response or covariate. In this paper, we consider the adequacy check for the linear regression model with the response and covariates missing simultaneously. We apply model adjustment and inverse probability weighting methods to deal with the missingness of response and covariate, respectively. In order to avoid the curse of dimension, we propose an empirical process test with the linear indicator weighting function. The asymptotic properties of the proposed test under the null, local and global alternative hypothetical models are rigorously investigated. A consistent wild bootstrap method is developed to approximate the critical value. Finally, simulation studies and real data analysis are performed to show that the proposed method performed well.