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Universally Consistent K-Sample Tests via Dependence Measures.

Sambit Panda1, Cencheng Shen2, Ronan Perry1

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Summary
This summary is machine-generated.

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.

Keywords:
Dependence MeasureK-Sample TestingTesting Independence

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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.