TY - JOUR
T1 - One-way MANOVA for functional data via Lawley–Hotelling trace test
AU - Zhu, Tianming
AU - Zhang, Jin Ting
AU - Cheng, Ming Yen
N1 - Funding Information:
Research partially supported by the National University of Singapore Academic Research Fund [R-155-000-212-114] and the Research Grants Council General Research Fund [12304120, 12302621]. The authors thank two reviewers for their constructive comments and suggestions which help improve the article substantially.
Publisher Copyright:
© 2022 Elsevier Inc.
PY - 2022/11
Y1 - 2022/11
N2 - 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.
AB - 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.
KW - Lawley–Hotelling trace test
KW - Multivariate functional data
KW - Root-n consistency
KW - Welch–Satterthwaite χ2 -approximation
KW - χ2 -type mixtures
UR - http://www.scopus.com/inward/record.url?scp=85138044192&partnerID=8YFLogxK
U2 - 10.1016/j.jmva.2022.105095
DO - 10.1016/j.jmva.2022.105095
M3 - Journal article
SN - 0047-259X
VL - 192
JO - Journal of Multivariate Analysis
JF - Journal of Multivariate Analysis
M1 - 105095
ER -