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Title: Asymptotic Normality of Entropy Estimators
Author: Zhang, Xing
Date Created: 2013
Description: 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 sufficien...

Title: Asymptotic Normality of Entropy Estimators
Author: Zhang, Xing
Date Created: 2013
Description: 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 sufficien...

Title: SEVERAL STATISTICAL RESULTS UNDER MULTINOMIAL DISTRIBUTION WITH INFINITE CATEGORIES
Author: Zhou, Jun
Date Created: 2009
Description: This dissertation discusses several statistical results under multinomial distribution with infinite categories. Firstly, the discussion focuses on Simpson's diversity index and Turing's formula. We established an unbiased estimate for the newly p...