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

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.