A doubly robust goodness-of-fit test in general linear models with missing covariates

In this article, we utilize a form of general linear model where missing data occurred randomly on the covariates. We propose a test function based on the doubly robust method to investigate goodness of fit of the model. For this aim, kernel method is used to estimate unknown functions under estimating equation method. Doubly robustness and asymptotic properties of the test function are obtained under local and alternative hypotheses. Furthermore, we investigate the power of the proposed test function by means of some simulation studies and finally we apply this method on analyzing a real dataset.