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Asymptotic Normality of Entropy Estimators
Title
Asymptotic Normality of Entropy Estimators
Author
Zhang, Xing
Date Created
2013
Subjects--Topical
Mathematics
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...
Goodness-of-Fit Tests Under Permutations
Title
Goodness-of-Fit Tests Under Permutations
Author
Chen, Chen
Date Created
2019
Subjects--Topical
Statistics, Mathematics, Information science
Description
Several new goodness-of-fit tests are proposed on countable alphabets, where certain fundamental statistical concepts associated with random variables, such as cumulative distribution functions, characteristic functions and moments, may not exist....
Jensen-Shannon Divergence: Estimation and Hypothesis Testing
Title
Jensen-Shannon Divergence: Estimation and Hypothesis Testing
Author
Stewart, Ann
Date Created
2019
Subjects--Topical
Statistics
Description
Jensen-Shannon divergence is one reasonable solution to the problem of measuring the level of difference or "distance'" between two probability distributions on a multinomial population. If one of the distributions is assumed to be known a priori,...
SEVERAL STATISTICAL RESULTS UNDER MULTINOMIAL DISTRIBUTION WITH INFINITE CATEGORIES
Title
SEVERAL STATISTICAL RESULTS UNDER MULTINOMIAL DISTRIBUTION WITH INFINITE CATEGORIES
Author
Zhou, Jun
Date Created
2009
Subjects--Topical
Statistics, Mathematics
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...