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Saddlepoint approximations for the P-values and probability mass functions of some bivariate sign tests

Author

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  • Abd El-Raheem M. Abd El-Raheem
  • Ibrahim A. A. Shanan
  • Ehab F. Abd-Elfattah

Abstract

Bivariate analysis is essential in several applied fields, such as medicine, engineering, biology, and econometrics. Many parametric and non-parametric procedures can be used for bivariate analysis. Non-parametric procedures require fewer conditions than their parametric counterparts. Therefore, this article proposes an accurate approximation of the p-values and the probability mass functions of some non-parametric bivariate tests, including bivariate sign tests and medians. The proposed approximation, saddlepoint approximation, is compared to the traditional approximation method, asymptotic normal approximation method, and Edgeworth expansion through three real data examples and a simulation study. The numerical results show that the proposed approximation method is more accurate than the asymptotic method and Edgeworth expansion. Furthermore, it is computationally less demanding than the simulation method, which is permutation-based and time-consuming.

Suggested Citation

  • Abd El-Raheem M. Abd El-Raheem & Ibrahim A. A. Shanan & Ehab F. Abd-Elfattah, 2024. "Saddlepoint approximations for the P-values and probability mass functions of some bivariate sign tests," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 53(24), pages 8942-8953, December.
    • Handle: RePEc:taf:lstaxx:v:53:y:2024:i:24:p:8942-8953
    DOI: 10.1080/03610926.2024.2315293
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