Zhu, Tianming; Zhang, Jin-Ting; Cheng, Ming-Yen One-way MANOVA for functional data via Lawley-Hotelling trace test. (English) Zbl 1520.62098 J. Multivariate Anal. 192, Article ID 105095, 20 p. (2022). Summary: Functional data arise from various fields of study and there have been numerous works on their analysis. However, most of existing methods consider the univariate case and methodology for multivariate functional data analysis is rather limited. In this article, we consider testing equality of vectors of mean functions for multivariate functional data, i.e., functional one-way multivariate analysis of variance (MANOVA). To this aim, we study asymptotic null distribution of the functional Lawley-Hotelling trace (FLH) test statistic and approximate it by a Welch-Satterthwaite type \(\chi^2\)-approximation. We describe two approaches to estimating the parameters in the \(\chi^2\)-approximation ratio-consistently. The resulting FLH test has the correct asymptotic level, is root-\(n\) consistent in detecting local alternatives, and is computationally efficient. The numerical performance is examined via some simulation studies and application to three real data examples. The proposed FLH test is comparable with four existing tests based on permutation in terms of size control and power. The major advantage is that it is much faster to compute. Cited in 1 Document MSC: 62J10 Analysis of variance and covariance (ANOVA) 62H15 Hypothesis testing in multivariate analysis 62R10 Functional data analysis Keywords:\(\chi^2\)-type mixtures; Lawley-Hotelling trace test; multivariate functional data; root-\(n\) consistency; Welch-Satterthwaite \(\chi^2\)-approximation Software:fda (R) PDFBibTeX XMLCite \textit{T. Zhu} et al., J. Multivariate Anal. 192, Article ID 105095, 20 p. 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