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A maximum statistic for the one-sided location-scale alternative in the two-stage design

Author

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  • Hidetoshi Murakami

    (Tokyo University of Science)

  • Markus Neuhäuser

    (Koblenz University of Applied Sciences)

Abstract

An increase in location is typically accompanied by an increase in variability. Subsequently, the heteroscedasticity can indicate a treatment effect. Therefore, it may be appropriate to perform a location-scale test. A common statistic for a location-scale test is the sum of a location and scale statistic. As demonstrated by Neuhäuser (Biometri J 43:809–819, 2001), weighting the sum increases the power. Although weights cannot usually be reasonably selected a priori, a weighting is possible in an adaptive design using the information obtained in an interim analysis. Here, we propose an adaptive statistic that increases and stabilizes the power. The power performance in various situations for continuous and discrete distributions is investigated using Monte Carlo simulations, which reveal that the proposed statistic increases and stabilizes the power, thus rendering it a strong competitor to existing location-scale statistics. The new statistic is illustrated using real data.

Suggested Citation

  • Hidetoshi Murakami & Markus Neuhäuser, 2025. "A maximum statistic for the one-sided location-scale alternative in the two-stage design," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 34(1), pages 91-112, March.
    • Handle: RePEc:spr:stmapp:v:34:y:2025:i:1:d:10.1007_s10260-024-00775-9
    DOI: 10.1007/s10260-024-00775-9
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    References listed on IDEAS

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    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. Marco Marozzi, 2013. "Adaptive choice of scale tests in flexible two-stage designs with applications in experimental ecology and clinical trials," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(4), pages 747-762.
    4. Murakami, Hidetoshi, 2007. "Lepage type statistic based on the modified Baumgartner statistic," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 5061-5067, June.
    5. 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.
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