AI 中文总结
本文针对有限支撑离散随机变量的三类外熵插件估计器推导一阶偏差公式，提出偏差校正方法，经模拟验证其有限样本性能更优，支持渐近场景中使用未校正插件估计器。
AI 中文摘要
本文研究有限支撑离散随机变量的Shannon、Rényi及Tsallis外熵插件估计器的有限样本偏差。通过分析中间泛函S_α=∑_(i=1)^r (1-p_i)^α的偏差，推导得到这三类估计器的显式一阶偏差公式，进而提出偏差校正后的估计器。研究表明，未校正与校正后的估计器渐近等价，仅相差O(1/n)阶项。模拟研究验证了理论结果，证实偏差校正估计器的有限样本性能更优。所得结果支持在渐近场景（如关于几乎必然收敛与渐近正态性的配套论文所考虑的场景）中使用更简单的未校正插件估计器。
英文摘要
This paper studies the finite-sample bias of plug-in estimators for Shannon, Rényi, and Tsallis extropies for finitely supported discrete random variables. We derive explicit first-order bias formulas for all three estimators by analyzing the bias of the intermediate functional S_α= \sum_{i=1}^r (1-p_i)^α. Bias-corrected estimators are then proposed. We show that the uncorrected and corrected estimators are asymptotically equivalent, differing only by terms of order O(1/n). A simulation study validates the theoretical results and demonstrates the superior finite-sample performance of the bias-corrected estimators. The results justify the use of the simpler uncorrected plug-in estimators in asymptotic settings, such as those considered in the companion paper on almost sure convergence and asymptotic normality.
Comments13 pages, 5 figures. Companion paper to "Nonparametric Estimation of Extropy, Rényi Extropy, and Tsallis Extropy: Almost Sure Convergence and Asymptotic Normality" (arXiv:79616144 [stat.ME])
