Entropy-based test for generalised Gaussian distributions

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ÇADIRCI M. S., Evans D., Leonenko N., Makogin V.

Computational Statistics and Data Analysis, cilt.173, 2022 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 173
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1016/j.csda.2022.107502
  • Dergi Adı: Computational Statistics and Data Analysis
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Biotechnology Research Abstracts, INSPEC, zbMATH, DIALNET
  • Anahtar Kelimeler: Generalised Gaussian distribution, Goodness-of-fit test, Maximum entropy principle, Nearest neighbour estimator of entropy, Shannon entropy
  • Sivas Cumhuriyet Üniversitesi Adresli: Evet

Özet

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.