Self‐Normalising Tests Using the Cauchy Distribution
提出一种检验方法，统计量为两个加权平均值的比值，在原假设下收敛于标准柯西分布，且无需估计尺度参数，适用于一般设定检验，可扩展到相关样本的多变量框架。
ABSTRACT A testing principle is introduced where the statistic is the ratio of two weighted averages. The ratio converges to the standard Cauchy distribution under the null hypothesis. At the same time, a potential nuisance scaling parameter cancels from the ratio without having to be estimated, making these Cauchy tests self‐normalising. These tests are not directed against specific alternatives and belong to the toolkit of general specification testing. We indicate how Cauchy tests can be extended to a multivariate framework of correlated samples, such that the tests are robust with respect to cross‐dependence without the need to explicitly account for it.