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

Luai Al-Labadi (), Ruodie Yu and Kairui Bao
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Luai Al-Labadi: Department of Mathematics and Statistics, American University of Sharjah, Sharjah 26666, United Arab Emirates
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

Stats, 2025, vol. 8, issue 4, 1-15

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.

Keywords: bootstrap; empirical likelihood; goodness-of-fit test; local linear estimator; model assessment; sample entropy (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2025
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