论文信息 - Normal Laws for Two Entropy Estimators on Infinite Alphabets

Normal Laws for Two Entropy Estimators on Infinite Alphabets

This paper offers sufficient conditions for the Miller–Madow estimator and the jackknife estimator of entropy to have respective asymptotic normalities on countably infinite alphabets.

Chen Chen | Jialin Zhang | Zhiyi Zhang | Michael Grabchak | Ann Stewart

[1] Sang Joon Kim,et al. A Mathematical Theory of Communication , 2006 .

[2] Thomas M. Cover,et al. Elements of Information Theory , 2005 .

[3] S. Zahl,et al. JACKKNIFING AN INDEX OF DIVERSITY , 1977 .

[4] Zhiyi Zhang,et al. Statistical Implications of Turing's Formula , 2016 .

[5] Thomas M. Cover,et al. Elements of information theory (2. ed.) , 2006 .

[6] A. Antos,et al. Convergence properties of functional estimates for discrete distributions , 2001 .

[7] B. Harris. The Statistical Estimation of Entropy in the Non-Parametric Case , 1975 .

[8] Thorsten Gerber,et al. Handbook Of Mathematical Functions , 2016 .

[9] Liam Paninski,et al. Estimation of Entropy and Mutual Information , 2003, Neural Computation.

[10] Zhiyi Zhang,et al. Bias Adjustment for a Nonparametric Entropy Estimator , 2013, Entropy.

[11] J. Geluk. Π-regular variation , 1981 .

[12] Xing Zhang,et al. A Normal Law for the Plug-in Estimator of Entropy , 2012, IEEE Transactions on Information Theory.