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A KL-divergence-based test for elliptical distribution
Yin Tang1, Yanyuan Ma2, Bing Li2
1Dr. Bing Zhang Department of Statistics, University of Kentucky, USA.
Journal of Nonparametric Statistics
|April 2, 2026
Summary
This study introduces a new KL-divergence test for elliptical distributions, considering both direction and length properties. The novel method, using k-nearest neighbors, shows improved performance over existing techniques.
Area of Science:
- Statistics
- Probability Theory
Background:
- Elliptical distributions are fundamental in multivariate statistics.
- Testing these distributions is crucial for various data analyses.
Purpose of the Study:
- To develop a novel KL-divergence based procedure for testing elliptical distributions.
- To account for the independence of length and direction, and uniform direction properties.
Main Methods:
- Constructing a test statistic using the k-nearest neighbors (kNN) method.
- Considering cases with known and unknown mean vectors and covariance matrices.
- Establishing asymptotic properties using sample splitting, truncation, and transformations.
Main Results:
- Rigorously established first-order asymptotic properties of the test statistic.
- Proposed debiasing and variance inflation techniques to address influence function degeneration.
- Numerical implementations demonstrated superior size and power performance compared to existing methods.
Conclusions:
- The proposed KL-divergence based procedure offers a robust and effective method for testing elliptical distributions.
- The novel approach provides better statistical performance than current state-of-the-art procedures.
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