Asymptotic Properties of a Statistical Estimator of the Jeffreys Divergence: The Case of Discrete Distributions
Year: 2024
Type: article
Abstract: 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.
Source: Mathematics
DOI: 10.3390/math12213319
Institutions: The Russian Presidential Academy of National Economy and Public Administration, Novosibirsk State University of Economics and Management, Novosibirsk State Technical University, Siberian State University Geosystems and Technology, Imperial College London, National University of Engineering, Universidade de São Paulo
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,955
OpenAlex ID: W4403682743