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Diagnostic Tools for Exploring Differences in Distributional Properties Between Two Samples: Nonparametric Approach

In: Asymptotic and Methodological Statistics

Author

Listed:
  • Bogdan Ćmiel

    (AGH University of Krakow, Faculty of Applied Mathematics)

  • Teresa Ledwina

    (Polish Academy of Sciences, Institute of Mathematics)

Abstract

This paper reconsiders the problem of testing the equality of two unspecified continuous distributions. The framework, which we propose, allows for readable and insightful data visualisation and helps to understand and quantify how two groups of data differ. We consider a useful weighted rank empirical process on (0, 1) and utilise a grid-based approach, based on diadic partitions of (0, 1), to discretize the continuous process and construct local simultaneous acceptance regions. These regions help to identify statistically significant deviations from the null model. In addition, the form of the process and its dicretization lead to a highly interpretable visualisation of distributional differences. We also introduce a new two-sample test, explicitly related to the visualisation. Numerical studies show that the new test procedure performs very well. We illustrate the use and diagnostic capabilities of our approach by an application to a known set of neuroscience data.

Suggested Citation

  • Bogdan Ćmiel & Teresa Ledwina, 2026. "Diagnostic Tools for Exploring Differences in Distributional Properties Between Two Samples: Nonparametric Approach," Springer Books, in: Daniel Hlubinka & Šárka Hudecová & Matúš Maciak & Michal Pešta (ed.), Asymptotic and Methodological Statistics, chapter 0, pages 357-380, Springer.
    • Handle: RePEc:spr:sprchp:978-3-032-07178-1_18
    DOI: 10.1007/978-3-032-07178-1_18
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