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Energy statistic-based modified information criterion for detecting the change in distribution.

Joseph Njuki¹, Wei Ning²

¹Department of Mathematics and Statistics, Coastal Carolina University, Conway, SC, USA.

Journal of Applied Statistics

|June 4, 2026

Summary

A new nonparametric test, the Energy statistics-based modified information criterion (EMIC), is proposed for detecting changes in random variable sequences. This EMIC method demonstrates superior performance, particularly for changes in the middle of data sequences.

Keywords:

62-08 62E20 62G30 Change point detection energy statistics modified information criterion non-parametric tests

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Area of Science:

Statistics
Change Point Detection
Nonparametric Methods

Background:

Detecting changes in the distribution of independent random variables is crucial in various scientific fields.
Existing methods may have limitations in detecting changes, especially when they occur within a sequence.

Purpose of the Study:

To propose a novel nonparametric test for detecting change points in the distribution of independent random variables.
To introduce the Energy statistics-based modified information criterion (EMIC) for enhanced change point detection.

Main Methods:

Developed a nonparametric test by leveraging the relationship between U-statistics and Energy statistics (V-statistics).
Utilized a modified information criterion (MIC) within the Energy statistics framework for change point detection (EMIC).
Conducted simulation studies to assess finite sample properties, efficiency, and power compared to existing methods.

Main Results:

The proposed EMIC test procedure and change point location estimator are consistent under the alternative hypothesis.
Simulation results indicate that the EMIC method outperforms other approaches, especially when changes occur near the sequence's midpoint.
The method's effectiveness was demonstrated in real-life applications for detecting changes in mean and variance.

Conclusions:

The EMIC method offers a robust and effective approach for nonparametric change point detection.
This method shows particular strength in identifying shifts occurring in the central part of a data sequence.
The EMIC test has practical utility in analyzing real-world data for detecting distributional changes.