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

Bogdan Ćmiel () and Teresa Ledwina ()
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Bogdan Ćmiel: AGH University of Krakow, Faculty of Applied Mathematics
Teresa Ledwina: Polish Academy of Sciences, Institute of Mathematics

Chapter Chapter 18 in Asymptotic and Methodological Statistics, 2026, pp 357-380 from Springer

Abstract: 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.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-032-07178-1_18

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DOI: 10.1007/978-3-032-07178-1_18

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