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

作     者：Sattler, Paavo Rosenbaum, Manuel 

作者机构：Tech Univ Dortmund Inst Math Stat & Ind Applicat Fac Stat Joseph Von Fraunhofer Str 2-4 D-44221 Dortmund Germany Ulm Univ Inst Stat Helmholtzstr 20 D-89081 Ulm Germany 

出 版 物：《STATISTICS & PROBABILITY LETTERS》 (Stat. Probab. Lett.)

年 卷 期：2025年第219卷

核心收录：

学科分类：07[理学] 0714[理学-统计学（可授理学、经济学学位）] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Multivariate statistic Computational effort Hypothesis matrix Anova-type-statistic Quadratic-forms 

摘      要：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 B is an element of R d . 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 HB = y can be expressed by various hypothesis matrices H is an element of R m x d and corresponding vectors y is an element of R m , 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-typestatistic, for each hypothesis HB = 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.