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Two-Sample Tests Based on Data Depth.

Xiaoping Shi1, Yue Zhang1, Yuejiao Fu2

  • 1Department of Computer Science, Mathematics, Physics and Statistics, University of British Columbia, Kelowna, BC V1V 1V7, Canada.

Entropy (Basel, Switzerland)
|February 25, 2023
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Summary
This summary is machine-generated.

This study introduces two novel statistical tests for multivariate homogeneity, enhancing the ability to determine if samples originate from the same distribution. These new methods show superior performance in simulations for this crucial data analysis task.

Keywords:
asymptotic distributiondata depthhypothesis testmulti-sample problemnon-parametric tests

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Area of Science:

  • Multivariate statistics
  • Statistical hypothesis testing
  • Data analysis

Background:

  • Homogeneity testing is crucial for comparing multivariate samples.
  • Existing data depth-based tests may lack sufficient power.
  • Data depth is increasingly recognized in quality assurance.

Purpose of the Study:

  • To propose two new test statistics for the multivariate two-sample homogeneity test.
  • To evaluate the performance of these novel statistics.
  • To discuss the extension to multisample scenarios.

Main Methods:

  • Development of two new test statistics based on data depth.
  • Asymptotic null distribution analysis (χ2(1)).
  • Simulation studies to compare performance.

Main Results:

  • The proposed test statistics share a χ2(1) asymptotic null distribution.
  • Simulation studies indicate superior performance compared to existing methods.
  • The tests are generalizable to multivariate multisample situations.

Conclusions:

  • The new data depth-based tests offer improved power for multivariate homogeneity testing.
  • The proposed methodology is applicable to both two-sample and multisample problems.
  • Demonstrated utility through real-world data examples.