Asymptotic Normality of Entropy Estimators

1 online resource (32 pages) : PDF

2013

University of North Carolina at Charlotte

Shannon's entropy plays a central role in many fields of mathematics. In the first chapter, we present a sufficient condition for the asymptotic normality of the plug-in estimator of Shannon's entropy defined on a countable alphabet. The sufficient condition covers a range of cases with countably infinite alphabets, for which no normality results were previously known. In the second chapter of this dissertation, we establish the asymptotic normality of a recently introduced non-parametric entropy estimator under another sufficient condition.The proposed estimator, developed in Turing's perspective, is known for its improved estimation accuracy.

doctoral dissertations

Mathematics

Ph.D.

Asymptotic Normality
Entropy
Nonparametric Entropy Estimation
Turing's Formula

Applied Mathematics

Zhang, Zhiyi

Sun, Yanqing
Jiang, Jiancheng
Zheng, Yuliang

Thesis (Ph.D.)--University of North Carolina at Charlotte, 2013.

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Zhang_uncc_0694D_10428

http://hdl.handle.net/20.500.13093/etd:1120