Entropy-based goodness-of-fit testsfor multivariate distributions
Başlık çevirisi mevcut değil.
- Tez No: 760265
- Danışmanlar: Belirtilmemiş.
- Tez Türü: Doktora
- Konular: Matematik, Mathematics
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 2021
- Dil: İngilizce
- Üniversite: University of Wales-Cardiff
- Enstitü: Yurtdışı Enstitü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 142
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Özet (Çeviri)
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 L 2 -consistence.
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