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Powerful goodness‐of‐fit tests based on the likelihood ratio

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  • Jin Zhang

Abstract

Summary. A new approach of parameterization is proposed to construct a general goodness‐of‐fit test. It can not only generate traditional tests (including the Kolmogorov–Smirnov, Cramér–von Mises and Anderson–Darling tests) but also produce new types of omnibus tests, which are generally much more powerful than the old ones.

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  • Jin Zhang, 2002. "Powerful goodness‐of‐fit tests based on the likelihood ratio," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 281-294, May.
    • Handle: RePEc:bla:jorssb:v:64:y:2002:i:2:p:281-294
    DOI: 10.1111/1467-9868.00337
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    Cited by:

    1. Lykou, R. & Tsaklidis, G. & Papadimitriou, E., 2020. "Change point analysis on the Corinth Gulf (Greece) seismicity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    2. Jesse Frey, 2008. "An exact distribution-free one-sample test for equivalence," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(8), pages 739-750.
    3. Zhang, Jin & Wu, Yuehua, 2007. "k-Sample tests based on the likelihood ratio," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4682-4691, May.
    4. Coin, Daniele, 2008. "A goodness-of-fit test for normality based on polynomial regression," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 2185-2198, January.
    5. 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.
    6. J. I. Beltrán-Beltrán & F. J. O’Reilly, 2019. "On goodness of fit tests for the Poisson, negative binomial and binomial distributions," Statistical Papers, Springer, vol. 60(1), pages 1-18, February.
    7. Meintanis, S.G. & Milošević, B. & Jiménez–Gamero, M.D., 2024. "Goodness–of–fit tests based on the min–characteristic function," Computational Statistics & Data Analysis, Elsevier, vol. 197(C).
    8. M. Cockeran & S. G. Meintanis & L. Santana & J. S. Allison, 2021. "Goodness-of-fit testing of survival models in the presence of Type–II right censoring," Computational Statistics, Springer, vol. 36(2), pages 977-1010, June.
    9. Wolfgang Rolke & Cristian Gutierrez Gongora, 2021. "A chi-square goodness-of-fit test for continuous distributions against a known alternative," Computational Statistics, Springer, vol. 36(3), pages 1885-1900, September.
    10. Xu, Xingzhong & Ding, Xiaobo & Zhao, Shuran, 2009. "New goodness-of-fit tests based on fiducial empirical distribution function," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1132-1141, February.
    11. L. Ndwandwe & J. S. Allison & L. Santana & I. J. H. Visagie, 2023. "Testing for the Pareto type I distribution: a comparative study," METRON, Springer;Sapienza Università di Roma, vol. 81(2), pages 215-256, August.
    12. J. S. Allison & L. Santana & N. Smit & I. J. H. Visagie, 2017. "An ‘apples to apples’ comparison of various tests for exponentiality," Computational Statistics, Springer, vol. 32(4), pages 1241-1283, December.
    13. Zhang, Jin & Wu, Yuehua, 2005. "Likelihood-ratio tests for normality," Computational Statistics & Data Analysis, Elsevier, vol. 49(3), pages 709-721, June.
    14. Jingjing Qu & Hon Keung Tony Ng & Chul Moon, 2024. "Empirical likelihood ratio tests for homogeneity of component lifetime distributions based on system lifetime data," Computational Statistics, Springer, vol. 39(6), pages 3007-3029, September.

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