Tests for equality of several mean vector functions for multivariate functional data with applications

Zhiping Qiu, Jiangyuan Fan and Jin-Ting Zhang

Journal of Nonparametric Statistics, 2025, vol. 37, issue 4, 1070-1090

Abstract: In various scientific and technological fields, it is common to encounter multivariate functional data, where continuous vector functions for statistical units are observed over a specific interval. This paper aims to investigate the equality of mean vector functions in multi-sample multivariate functional data. To accomplish this, two novel global testing statistics are introduced by integrating or maximising the pointwise Lawley-Hotelling trace test statistic. The paper also provides asymptotic expressions for these proposed testing statistics under the null hypothesis and establishes their consistency with respect to the square root of the sample size. The performance of the two new testing procedures is demonstrated through simulation studies and the analysis of a real-world data example, highlighting their advantages over existing methods.

Date: 2025
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DOI: 10.1080/10485252.2024.2396361

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