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Testing the distribution change in multivariate data using rank energy statistics
Yanhong Liu1, Jiaqi Li2, Zhonghua Li3
1Guangzhou Institute of International Finance, Guangzhou University, Guangzhou, People's Republic of China.
Journal of Applied Statistics
|July 31, 2026
Summary
This study introduces a new nonparametric test for detecting single distribution changes in multivariate data. The novel rank energy statistic offers a distribution-free property, enabling robust change point detection even in complex financial datasets.
Area of Science:
- Statistics
- Data Analysis
Background:
- Detecting distribution changes in multivariate data is crucial for time series analysis.
- Existing methods may lack robustness or computational efficiency, especially with complex data.
Purpose of the Study:
- To develop a novel nonparametric test for detecting and locating a single change point in multivariate data.
- To ensure the test is computationally feasible and robust across various data distributions.
Main Methods:
- A novel rank energy statistic based on multivariate ranks derived from measure transportation theory.
- Theoretical analysis of asymptotic null distribution for distribution-free properties.
- Development of a computationally feasible algorithm for universal rejection thresholds.
Main Results:
- The proposed test exhibits an exact distribution-free property, independent of the data-generating distribution.
- A consistent theory for estimated change point location was established.
- Extensive simulations demonstrated robust performance, particularly with heavy-tailed distributions.
Conclusions:
- The developed nonparametric test effectively detects and locates distribution changes in multivariate data.
- The test's distribution-free nature and computational feasibility make it broadly applicable, including to financial data analysis.
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