Intersection-Union Model Specification Test with Response Missing at Random

When the response variables are missing randomly, in the process of statistical inference of the parameters of interest, two common working models are the regression function model and the selection probability model. In order to avoid the inference bias caused by the model setting error, the regression function model and selection probability models are necessary and meaningful for model testing. For this reason, for the first time in this paper, the feature functions are applied to the model testing problem of random missing response variables and discrete variable response variables, and a Euclidean distance between sample points is constructed based on test statistic. The proposed test avoids the selection of smoothing parameters such as bandwidth, and at the same time can detect the local alternative hypothesis at the fastest parameter speed. Further, this paper aims at the composite null hypothesis: at least one of the two working models is designed. It is correct, and a test method of the merged model is proposed. An important application scenario of this test is to determine whether the bistable estimation of the parameter is a coincident estimate. This article deeply studies the test of the merged model in the original hypothesis, the global alternative hypothesis, and the local alternative hypothesis. The asymptotic property of the following, and using the boostrap method to determine the rejection domain of the test, study the performance of the merge model test under a limited sample. Finally, this article applies the proposed merge model test method to analyze the clinical research of AIDS research Test Data. It is worth mentioning that the combined model test mentioned in this article not only has good performance, but also the method is simple and easy to implement, and the corresponding p-value is easy to calculate.