Search results | J. Murrey Atkins Library

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...

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....

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,...

Title: Non-parametric Estimation of Information-theoretic Quantities in Entropic Perspective
Author: Zhang, Jialin
Date Created: 2019
Subjects--Topical: Statistics
Description: Introduced by Shannon, mutual information is a fundamental brick of information theory for its essential role in measuring association on non-ordinal alphabets. Mutual information being zero is a golden property as it indicates a probabilistic ind...

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...