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Entropy-based test for generalised Gaussian distributions

Author

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

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.

Suggested Citation

  • Cadirci, Mehmet Siddik & Evans, Dafydd & Leonenko, Nikolai & Makogin, Vitalii, 2022. "Entropy-based test for generalised Gaussian distributions," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    • Handle: RePEc:eee:csdana:v:173:y:2022:i:c:s0167947322000822
    DOI: 10.1016/j.csda.2022.107502
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    1. Alexander Bulinski & Denis Dimitrov, 2021. "Statistical Estimation of the Kullback–Leibler Divergence," Mathematics, MDPI, vol. 9(5), pages 1-36, March.
    2. G. Aulogiaris & K. Zografos, 2004. "A maximum entropy characterization of symmetric Kotz type and Burr multivariate distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(1), pages 65-83, June.
    3. Gonzales-Manteiga, Wenceslao & Martinez-Miranda, Maria Dolores & Van Keilegom, Ingrid, 2016. "Goodness-of-fit test in parametric mixed effects models based on estimation of the error distribution," LIDAM Reprints ISBA 2016010, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Shin, Seung Jun & Artemiou, Andreas, 2017. "Penalized principal logistic regression for sparse sufficient dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 111(C), pages 48-58.
    5. Kano, Y., 1994. "Consistency Property of Elliptic Probability Density Functions," Journal of Multivariate Analysis, Elsevier, vol. 51(1), pages 139-147, October.
    6. Wenceslao González-Manteiga & María Dolores Martínez-Miranda & Ingrid Van Keilegom, 2016. "Goodness-of-fit test in parametric mixed effects models based on estimation of the error distribution," Biometrika, Biometrika Trust, vol. 103(1), pages 133-146.
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