What does this research mean for the field?

A novel Kullback-Leibler divergence estimator based on k-nearest neighbor Shannon entropy provides an effective goodness-of-fit test for multivariate normality with accurate Type I error control and strong empirical power. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

This research focuses on estimating Kullback–Leibler divergence using Shannon entropy and developing a corresponding goodness-of-fit test.

June 27, 2026EntropyOpen Access

A New Estimator of Kullback–Leibler Divergence via Shannon Entropy

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Authors

MÇMehmet Sıddık ÇadırcıSivas Cumhuriyet Üniversitesi MSMartin SingullLinköping University

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Implication

Randomized trial examines KL divergence estimation in multivariate distributions, suggesting improved testing methods.

Key Points

This research focuses on estimating Kullback–Leibler divergence using Shannon entropy and developing a corresponding goodness-of-fit test.
Developed an estimator based on k-nearest neighbor (kNN) approaches and Shannon entropy derived from the Kozachenko–Leonenko method.
Proposed a KL-based test statistic reflecting the difference between fitted Gaussian entropy and kNN estimates.
Conducted Monte Carlo simulations for validation across various dimensions and sample sizes.
The proposed method maintains accurate Type I error control against non-Gaussian alternatives.
The test statistic converges to zero for multivariate normality, maintaining a positive bound for non-Gaussian cases.
Empirical power shows promising results across simulations, confirming the effectiveness of the method.

Cite This Study

Çadırcı et al. (2026) studied this question.

synapsesocial.com/papers/6a3f68f5aea7db3c1953fe69 https://doi.org/10.3390/e28070720

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A New Estimator of Kullback–Leibler Divergence via Shannon Entropy

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Key Points

Cite This Study

A New Estimator of Kullback–Leibler Divergence via Shannon Entropy

Discussion

Member takes

Implication

Key Points

Cite This Study

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