Abstract

In this article, we introduce two new test statistics based on pairwise distance to check whether a parametric model with missing response is correctly specified or not. The proposed test statistics are easy to implement and no non parametric function estimation is involved. The asymptotic properties of the newly introduced test statistics are investigated. Under the null hypothesis, it is shown that they converge to a non degenerate distribution. And it can also detect any local alternatives that are different from the null at the parametric rate. In addition, the convergence rates of the proposed test are unaffected by the dimension of covariates. Some simulation studies and a real data example are conducted to show the good performance of the proposed test.

摘要

在本文中，我们介绍了两个基于成对距离的新测试统计量，以检查是否正确指定了具有缺失响应的参数模型。所提出的检验统计易于实现，并且不涉及非参数函数估计。研究了新引入的检验统计量的渐近特性。在原假设下，表明它们收敛于非退化分布。并且它还可以检测任何与参数速率下的零值不同的局部替代方案。此外，所提出的检验的收敛速度不受协变量维数的影响。进行了一些模拟研究和真实数据示例，以显示所提出测试的良好性能。