Saddlepoint approximation for the p-values of some distribution-free tests

Abd El-Raheem M. Abd El-Raheem; Mona Hosny; Abd El-Raheem M. Abd El-Raheem; Mona Hosny

doi:10.3934/math.2025121

AIMS Mathematics

2025, Volume 10, Issue 2: 2602-2618. doi: 10.3934/math.2025121

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Saddlepoint approximation for the p-values of some distribution-free tests

Abd El-Raheem M. Abd El-Raheem ^{1
,
,},
Mona Hosny ²

1.
Department of Mathematics, Faculty of Education, Ain Shams University, Cairo 11566, Egypt
2.
Department of Mathematics, College of Science, King Khalid University, Abha, 61413, Saudi Arabia

Received: 24 September 2024 Revised: 07 January 2025 Accepted: 21 January 2025 Published: 13 February 2025
MSC : 62E17, 62G10

This article discusses the saddlepoint approximation for the p-values of some distribution-free tests, a signed rank test for bivariate location problems and a dispersion test for scale problems. The statistics of the two considered tests are constructed based on the ratio of two variables. The accuracy of the saddlepoint approximation is compared to traditional asymptotic normal approximation by applying numerical comparisons. Furthermore, the proposed approximations are illustrated by analyzing numerical examples. The results of numerical comparisons indicate that the approximation error resulting from the proposed method is much lower than the traditional method, which is evidence of the superiority of the proposed approximation method over the traditional method. Accordingly, we can say that the saddlepoint approximation method can be a competitive alternative to the traditional method.
- bivariate signed rank tests,
- location problems,
- saddlepoint approximations,
- scale problems
Citation: Abd El-Raheem M. Abd El-Raheem, Mona Hosny. Saddlepoint approximation for the p-values of some distribution-free tests[J]. AIMS Mathematics, 2025, 10(2): 2602-2618. doi: 10.3934/math.2025121

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Abstract

This article discusses the saddlepoint approximation for the p-values of some distribution-free tests, a signed rank test for bivariate location problems and a dispersion test for scale problems. The statistics of the two considered tests are constructed based on the ratio of two variables. The accuracy of the saddlepoint approximation is compared to traditional asymptotic normal approximation by applying numerical comparisons. Furthermore, the proposed approximations are illustrated by analyzing numerical examples. The results of numerical comparisons indicate that the approximation error resulting from the proposed method is much lower than the traditional method, which is evidence of the superiority of the proposed approximation method over the traditional method. Accordingly, we can say that the saddlepoint approximation method can be a competitive alternative to the traditional method.

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