Abstract

We propose a projection-based test to check logistic regression models when the dimension of the covariate vector may be divergent. The proposed test achieves a reduction in dimension, and the proposed method behaves as if only a single covariate is present. The test is shown to be consistent and can detect root-n local alternatives. We derive the asymptotic distribution of the proposed test under the null hypothesis and establish the test’s asymptotic behavior under the local and global alternatives. The numerical performance is remarkably attractive comparing to the existing methods. Real examples are presented for illustration. Supplementary materials for this article are available online.

摘要

当协变量向量的维数可能不同时，我们提出了一种基于投影的测试来检查逻辑回归模型。提议的测试实现了维度的减少，并且提议的方法表现得好像只存在一个协变量。该测试被证明是一致的，并且可以检测到 root- n本地替代方案。我们在原假设下推导出所提出检验的渐近分布，并在局部和全局备选方案下建立检验的渐近行为。与现有方法相比，数值性能非常有吸引力。提供真实示例以供说明。本文的补充材料可在线获取。