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The multi-aspect tests in the presence of ties

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  • Yamaguchi, Hikaru
  • Murakami, Hidetoshi

Abstract

The two-sample problem is one of the most important topics in various fields, such as biomedical experiments and product quality maintenance. The Lepage-type test, which is the sum of squares of standardized linear rank statistics, has often been used in the location-scale shift model. Recently, the Lepage-type test has been applied to the joint location-scale and joint location-scale-shape problems. In this study, the test statistics based on the Euclidean distance and Mahalanobis distance of standardized linear rank statistics are considered in the presence of ties. The moments of these test statistics are calculated by deriving the moment-generating function of the vector of linear rank statistics. Moreover, the gamma approximation based on these moments is compared with the chi-square approximation based on the limiting null distribution. Simulation studies and data examples demonstrate the usefulness of gamma approximation in the case of small sample sizes.

Suggested Citation

  • Yamaguchi, Hikaru & Murakami, Hidetoshi, 2023. "The multi-aspect tests in the presence of ties," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).
    • Handle: RePEc:eee:csdana:v:180:y:2023:i:c:s0167947322002602
    DOI: 10.1016/j.csda.2022.107680
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    References listed on IDEAS

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    1. Song, Zhi & Mukherjee, Amitava & Liu, Yanchun & Zhang, Jiujun, 2019. "Optimizing joint location-scale monitoring – An adaptive distribution-free approach with minimal loss of information," European Journal of Operational Research, Elsevier, vol. 274(3), pages 1019-1036.
    2. Amitava Mukherjee & Marco Marozzi, 2019. "A class of percentile modified Lepage-type tests," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(6), pages 657-689, August.
    3. Hidetoshi Murakami, 2016. "A moment generating function of a combination of linear rank tests and its asymptotic efficiency," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(4), pages 674-691, December.
    4. Mukherjee, Amitava & Sen, Rudra, 2018. "Optimal design of Shewhart–Lepage type schemes and its application in monitoring service quality," European Journal of Operational Research, Elsevier, vol. 266(1), pages 147-167.
    5. Liu, Huan & Tang, Yongqiang & Zhang, Hao Helen, 2009. "A new chi-square approximation to the distribution of non-negative definite quadratic forms in non-central normal variables," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 853-856, February.
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