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.

近年来，关于丢失数据的文献很多。它们中的大多数集中于仅缺少响应或协变量的情况。

在本文中，我们考虑了同时具有响应和协变量的线性回归模型的充分性检查。

我们应用模型调整和逆概率加权方法分别处理响应和协变量的缺失。为了避免维度的诅咒，我们提出了具有线性指标权重函数的经验过程测试。严格研究了在零，局部和全局替代假设模型下的拟议测试的渐近性质。开发了一致的野生自举方法来近似临界值。

最后，通过仿真研究和真实数据分析表明，该方法效果良好。