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Characterising transitive two-sample tests

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  • Lumley, Thomas
  • Gillen, Daniel L.

Abstract

Implicit in two-sample testing is the idea that a test consistently orders possible distributions. We characterise tests that are consistent with some ordering on distributions, showing all are tests for equality of some univariate real-valued functional in the two samples.

Suggested Citation

  • Lumley, Thomas & Gillen, Daniel L., 2016. "Characterising transitive two-sample tests," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 118-123.
    • Handle: RePEc:eee:stapro:v:109:y:2016:i:c:p:118-123
    DOI: 10.1016/j.spl.2015.11.005
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    References listed on IDEAS

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    1. B.M. Brown & T.P. Hettmansperger, 2002. "Kruskal–Wallis, Multiple Comparisons and Efron Dice," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 44(4), pages 427-438, December.
    2. Beardon, Alan F. & Candeal, Juan C. & Herden, Gerhard & Indurain, Esteban & Mehta, Ghanshyam B., 2002. "The non-existence of a utility function and the structure of non-representable preference relations," Journal of Mathematical Economics, Elsevier, vol. 37(1), pages 17-38, February.
    3. Toranzo, Margarita Estevez & Beloso, Carlos Herves, 1995. "On the existence of continuous preference orderings without utility representations," Journal of Mathematical Economics, Elsevier, vol. 24(4), pages 305-309.
    4. Monteiro, Paulo Klinger, 1987. "Some results on the existence of utility functions on path connected spaces," Journal of Mathematical Economics, Elsevier, vol. 16(2), pages 147-156, April.
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    Cited by:

    1. Olga V. Demler & Ilona A. Demler, 2023. "Non-Transitivity of the Win Ratio and the Area Under the Receiver Operating Characteristics Curve (AUC): a case for evaluating the strength of stochastic comparisons," Papers 2309.01791, arXiv.org, revised Sep 2023.

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