Problem
Research questions and friction points this paper is trying to address.
Chernoff Information
Bayesian Binary Hypothesis Testing
Nonparametric Estimation
Rényi Divergence
On the Estimation of Chernoff Information
🤖 AI Summary
本文解决了非参数条件下Chernoff信息难以估计的问题，通过重新表述优化条件并直接估计其导数，使用k-最近邻方法，提供了一种新的估计方法。
📝 Abstract
Chernoff information is a fundamental divergence measure characterizing the optimal error exponent in Bayesian binary hypothesis testing, with applications in information fusion, time-series analysis, and statistical learning theory. However, closed-form expressions exist only for simple parametric families, and nonparametric estimation remains difficult because the quantity is defined as an optimization of the unnormalized Rényi divergence over its order. We reformulate this optimization via a derivative condition, whose zero locates the optimal mixture parameter, and estimate the derivative directly using a $k$-nearest-neighbor method. We prove the $L_2$-consistency of the derivative estimator under mild regularity conditions on the densities and their domain. Coupled with a bisection procedure that locates the optimal parameter up to arbitrary precision, this yields an estimator for Chernoff information.
Innovation
Methods, ideas, or system contributions that make the work stand out.
derivative condition
k-nearest-neighbor method
L_2-consistency
bisection procedure
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