Entropy-based goodness-of-fit tests for multivariate distributions

Cadirci, Mehmet 2021. Entropy-based goodness-of-fit tests for multivariate distributions. PhD Thesis, Cardiff University. Item availability restricted.

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Abstract

Entropy is one of the most basic and significant descriptors of a probability distribution. It is still a commonly used measure of uncertainty and randomness in information theory and mathematical statistics. We study statistical inference for Shannon and Rényi’s entropy-related functionals of multivariate Gaussian and Student-t distributions. This thesis investigates three themes. First, we provide a non-parametric test of goodness-of-fit for a class of multivariate generalized Gaussian distributions based on maximum entropy principle via using the k-th nearest neighbour (NN) distance estimator of the Shannon entropy. Its asymptotic unbiasedness and consistency are demonstrated. Second, we show a class of estimators of the Rényi entropy based on an independent identical distribution sample drawn from an unknown distribution f on R m. We focus on the maximum Rényi entropy principle for multivariate Student-t and Pearson type II distributions. We also consider the entropy-based test for multivariate Student-t distribution using the k-th NN distances estimator of entropy and employ the properties of entropy estimators derived from NN distances. Third, we introduce a new classes of unimodal rotational invariant directional distributions, which generalize von Mises-Fisher distribution. We propose three types of distributions in which one of them represents the axial data. We provide all of the formula together with a short computational study of parameter estimators for each new type via the method of moments and method of maximum likelihood. We also offer the goodness-of-fit test to detect that the sample entries follow one of the introduced generalized von Mises-Fisher distribution based on the maximum entropy principle using the k-th NN distances estimator of Shannon entropy and to prove its L2 -consistence.

Item Type:	Thesis (PhD)
Date Type:	Completion
Status:	Unpublished
Schools:	Mathematics
Date of First Compliant Deposit:	18 November 2021
Last Modified:	10 Jun 2023 02:01
URI:	https://orca.cardiff.ac.uk/id/eprint/145616

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