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Choice of the hypothesis matrix for using the Anova-type-statistic

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  • Sattler, Paavo
  • Rosenbaum, Manuel

Abstract

Initially developed in Brunner et al. (1997), the Anova-type-statistic (ATS) is one of the most used quadratic forms for testing multivariate hypotheses for a variety of different parameter vectors θ∈Rd. Tests based on a version of the ATS are usually preferable over those based on other quadratic forms, like the Wald-type-statistic. However, the same null hypothesis Hθ=y can be expressed by various hypothesis matrices H∈Rm×d and corresponding vectors y∈Rm, yielding different values of the test statistic. Since this can entail differing test decisions, we investigate under which conditions certain tests using different hypothesis matrices coincide. In this manuscript, we show that for several versions of the Anova-type-statistic, for each hypothesis Hθ=y a companion matrix with a minimal number of rows can be constructed, testing the same hypothesis but also always yielding the same test decisions. This can substantially reduce computation time, as demonstrated in several conducted simulations.

Suggested Citation

  • Sattler, Paavo & Rosenbaum, Manuel, 2025. "Choice of the hypothesis matrix for using the Anova-type-statistic," Statistics & Probability Letters, Elsevier, vol. 219(C).
    • Handle: RePEc:eee:stapro:v:219:y:2025:i:c:s0167715225000021
    DOI: 10.1016/j.spl.2025.110356
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    References listed on IDEAS

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    1. Zhang, Jin-Ting & Guo, Jia & Zhou, Bu, 2017. "Linear hypothesis testing in high-dimensional one-way MANOVA," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 200-216.
    2. Paavo Sattler & Markus Pauly, 2024. "Testing hypotheses about correlation matrices in general MANOVA designs," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 33(2), pages 496-516, June.
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