Asymptotic Properties of a Statistical Estimator of the Jeffreys Divergence: The Case of Discrete Distributions
We investigate the asymptotic properties of the plug-in estimator for the Jeffreys divergence, the symmetric variant of the Kullback–Leibler (KL) divergence. This study focuses specifically on the divergence between discrete distributions. Traditionally, estimators rely on two independent samples corresponding to two distinct conditions. However, we propose a one-sample estimator where the condition results from a random event. We establish the estimator’s asymptotic unbiasedness (law of large numbers) and asymptotic normality (central limit theorem). Although the results are expected, the proofs require additional technical work due to the randomness of the conditions.
Authors
- Lyudmila Serga (ORCID: https://orcid.org/0000-0002-8934-8876)
- Vladimir Glinskiy (ORCID: https://orcid.org/0000-0002-7149-3020)
- Anatoly Yambartsev (ORCID: https://orcid.org/0000-0002-8398-1347)
- A. V. Logachov (ORCID: https://orcid.org/0000-0002-0605-8831)
- O. Logachova (ORCID: https://orcid.org/0000-0003-4994-5606)
- Helder Rojas (ORCID: https://orcid.org/0000-0002-6183-8929)
Institutions
- Universidade de São Paulo (BR)
- Novosibirsk State University of Economics and Management (RU)
- Siberian State University Geosystems and Technology (RU)
- Imperial College London (GB)
- National University of Engineering (PE)
- Novosibirsk State Technical University (RU)
Publication Details
- Journal
- Mathematics
- Published
- 2024-10-23
- DOI
- https://doi.org/10.3390/math12213319
- Primary Topic
- Statistical Mechanics and Entropy
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Fundação de Amparo à Pesquisa do Estado de São Paulo
- Russian Science Foundation