 Choice of the hypothesis matrix for using the Anova-type-statisticPaavo Sattler and Manuel Rosenbaum Statistics & Probability Letters, 2025, vol. 219, issue C 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. Keywords: Multivariate statistic; Computational effort; Hypothesis matrix; Anova-type-statistic; Quadratic-forms (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:219:y:2025:i:c:s0167715225000021 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spl.2025.110356 Access Statistics for this article Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul More articles in Statistics & Probability Letters from Elsevier |
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