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Goodness-of-Fit Tests via Entropy-Based Density Estimation Techniques

Author

Listed:
  • Luai Al-Labadi

    (Department of Mathematics and Statistics, American University of Sharjah, Sharjah 26666, United Arab Emirates
    Department of Mathematical & Computational Sciences, University of Toronto Mississauga, Mississauga, ON L5L 1C6, Canada)

  • Ruodie Yu

    (Department of Statistical Sciences, University of Toronto, Toronto, ON M5S 3G3, Canada)

  • Kairui Bao

    (Department of Statistical Sciences, University of Toronto, Toronto, ON M5S 3G3, Canada)

Abstract

Goodness-of-fit testing remains a fundamental problem in statistical inference with broad practical importance. In this paper, we introduce two new goodness-of-fit tests grounded in entropy-based density estimation techniques. The first is a boundary-corrected empirical likelihood ratio test, which refines the classic approach by addressing bias near the support boundaries, though, in practice, it yields results very similar to the uncorrected version. The second is a novel test built on Correa’s local linear entropy estimator, leveraging quantile regression to improve density estimation accuracy. We establish the theoretical properties of both test statistics and demonstrate their practical effectiveness through extensive simulation studies and real-data applications. The results show that the proposed methods deliver strong power and flexibility in assessing model adequacy in a wide range of settings.

Suggested Citation

  • Luai Al-Labadi & Ruodie Yu & Kairui Bao, 2025. "Goodness-of-Fit Tests via Entropy-Based Density Estimation Techniques," Stats, MDPI, vol. 8(4), pages 1-15, October.
    • Handle: RePEc:gam:jstats:v:8:y:2025:i:4:p:97-:d:1771049
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    References listed on IDEAS

    as
    1. Vexler, Albert & Gurevich, Gregory, 2010. "Empirical likelihood ratios applied to goodness-of-fit tests based on sample entropy," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 531-545, February.
    2. Wei Ning & Grace Ngunkeng, 2013. "An empirical likelihood ratio based goodness-of-fit test for skew normality," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(2), pages 209-226, June.
    3. Ebrahimi, Nader & Pflughoeft, Kurt & Soofi, Ehsan S., 1994. "Two measures of sample entropy," Statistics & Probability Letters, Elsevier, vol. 20(3), pages 225-234, June.
    4. Luai Al-Labadi & Zhirui Chu & Ying Xu, 2025. "Advancements in Rényi entropy and divergence estimation for model assessment," Computational Statistics, Springer, vol. 40(2), pages 633-650, February.
    5. Hadi Alizadeh Noughabi, 2015. "Empirical likelihood ratio-based goodness-of-fit test for the logistic distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(9), pages 1973-1983, September.
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