Universally Consistent K-Sample Tests via Dependence Measures
This provides a general framework for K-sample testing, allowing easy application of various dependence measures, but it is incremental as it builds on existing dependence measures.
The paper tackles the K-sample testing problem by showing that any dependence measure can be used for universally consistent testing via a transformation, enabling methods like distance correlation and Hilbert-Schmidt independence criterion to be applied.
The K-sample testing problem involves determining whether K groups of data points are each drawn from the same distribution. Analysis of variance is arguably the most classical method to test mean differences, along with several recent methods to test distributional differences. In this paper, we demonstrate the existence of a transformation that allows K-sample testing to be carried out using any dependence measure. Consequently, universally consistent K-sample testing can be achieved using a universally consistent dependence measure, such as distance correlation and the Hilbert-Schmidt independence criterion. This enables a wide range of dependence measures to be easily applied to K-sample testing.