One-way MANOVA for functional data via Lawley–Hotelling trace test

Tianming Zhu, Jin Ting Zhang, Ming Yen Cheng*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

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 χ2-approximation. We describe two approaches to estimating the parameters in the χ2-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.

Original languageEnglish
Article number105095
JournalJournal of Multivariate Analysis
Volume192
DOIs
Publication statusPublished - Nov 2022

Scopus Subject Areas

  • Numerical Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • Lawley–Hotelling trace test
  • Multivariate functional data
  • Root-n consistency
  • Welch–Satterthwaite  χ2 -approximation
  • χ2 -type mixtures

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