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Universally Consistent K-Sample Tests via Dependence Measures
Sambit Panda1, Cencheng Shen2, Ronan Perry1
1Department of Biomedical Engineering, Johns Hopkins University, Maryland, USA.
Statistics & Probability Letters
|October 28, 2024
Summary
This study introduces a transformation for K-sample testing, enabling the use of any dependence measure. This approach ensures universally consistent K-sample testing with measures like distance correlation.
Area of Science:
- Statistics
- Multivariate Analysis
Background:
- K-sample testing assesses if multiple data groups originate from the same distribution.
- Classical methods like ANOVA focus on mean differences, while newer methods address distributional differences.
Purpose of the Study:
- To develop a universal framework for K-sample testing.
- To enable the application of diverse dependence measures to K-sample testing problems.
Main Methods:
- Demonstration of a transformation enabling K-sample testing with arbitrary dependence measures.
- Utilizing universally consistent dependence measures such as distance correlation and Hilbert-Schmidt independence criterion.
Main Results:
- The proposed transformation allows any dependence measure to be applied to K-sample testing.
- Achieved universally consistent K-sample testing through the use of appropriate dependence measures.
Conclusions:
- The developed transformation provides a flexible and powerful approach to K-sample testing.
- This method broadens the applicability of various dependence measures in statistical analysis.
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