摘要
In this paper, we investigate the model checking problem for a general linear model with nonignorable missing covariates. We show that, without any parametric model assumption for the response probability, the least squares method yields consistent estimators for the linear model even if only the complete data are applied. This makes it feasible to propose two testing procedures for the corresponding model checking problem： a score type lack-of-fit test and a test based on the empirical process. The asymptotic properties of the test statistics are investigated. Both tests are shown to have asymptotic power 1 for local alternatives converging to the null at the rate n-r, 0 ≤ r 〈 1/2. Simulation results show that both tests perform satisfactorily.
In this paper, we investigate the model checking problem for a general linear model with nonignorable missing covariates. We show that, without any parametric model assumption for the response probability, the least squares method yields consistent estimators for the linear model even if only the complete data are applied. This makes it feasible to propose two testing procedures for the corresponding model checking problem： a score type lack-of-fit test and a test based on the empirical process. The asymptotic properties of the test statistics are investigated. Both tests are shown to have asymptotic power 1 for local alternatives converging to the null at the rate n-r, 0 ≤ r 〈 1/2. Simulation results show that both tests perform satisfactorily.
基金
supported by the National Natural Science Foundation of China (No. 10901162,10926073)
China Postdoctoral Science Foundation and the President Fund of GUCAS
the foundation of the Key Laboratory of Random Complex Structures and Data Science, CAS
supported by a research grant from the Research Committee, The Hong Kong Polytechnic University
