AI 中文总结
本文针对有限离散随机变量，提出外熵、α-Rényi外熵与α-Tsallis外熵的非参数估计方法，建立插件估计量的几乎处处收敛速度与渐近正态性，经模拟验证后为外熵类度量的实际应用提供了坚实基础。
AI 中文摘要
本文针对有限离散随机变量，提出了外熵及其扩展形式（α-Rényi外熵与α-Tsallis外熵）的非参数估计方法。我们为插件估计量建立了几乎处处收敛速度与渐近正态性，并通过全面的模拟研究验证了理论结果。该发现为外熵类度量在实际应用（包括预测、风险评估及不确定性下的决策）中的使用提供了坚实基础。
英文摘要
This paper proposes a nonparametric estimation procedure for extropy and its extensions, namely the α-Rényi and α-Tsallis extropies, for finite discrete random variables. We establish almost sure rates of convergence and asymptotic normality for the plug-in estimators. The theoretical results are validated through a comprehensive simulation study. The findings provide a solid foundation for the use of extropy-based measures in practical applications, including forecasting, risk assessment, and decision-making under uncertainty.
Comments19 pages, 5 figures. Submitted to a journal for publication. Companion paper on finite-sample bias correction also available
