Entropy-based test for generalised Gaussian distributions

Mehmet Siddik Cadirci, Dafydd Evans, Nikolai Leonenko and Vitalii Makogin

Computational Statistics & Data Analysis, 2022, vol. 173, issue C

Abstract: The proof of L2 consistency for the kth nearest neighbour distance estimator of the Shannon entropy for an arbitrary fixed k≥1 is provided. It is constructed the non-parametric test of goodness-of-fit for a class of introduced generalised multivariate Gaussian distributions based on a maximum entropy principle. The theoretical results are followed by numerical studies on simulated samples. It is shown that increasing of k improves the power of the introduced goodness of fit tests. The asymptotic normality of the test statistics is experimentally proven.

Keywords: Maximum entropy principle; Generalised Gaussian distribution; Shannon entropy; Nearest neighbour estimator of entropy; Goodness-of-fit test (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:173:y:2022:i:c:s0167947322000822

DOI: 10.1016/j.csda.2022.107502

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