Abstract

It is of great interest to test the equality of the means in two sam

ples of functional data. Past research has predominantly concentrated on lowdimensional functional data, a focus that may not hold in high-dimensional sce-

narios. In this article, we propose a novel two-sample test for the mean functions of high-dimensional functional data, employing a multi-resolution projec-

tion (MRP) method.

We establish the asymptotic normality of the proposed

MRP test statistic and investigate its power performance when the dimension of

the functional variables is high. In practice, functional data are observed only

at discrete and usually asynchronous points. We further explore the influence

of function reconstruction on the test statistic theoretically. Finally, we assess

the finite-sample performance of the proposed test through extensive simulation

studies and demonstrate its practicality via two real data applications. Specifically, our analysis of global climate data uncovers significant differences in the

functional means of climate variables in the years 2020-2069 when comparing intermediate greenhouse gas emission pathways (e.g., RCP4.5) to high greenhouse

gas emission pathways (e.g., RCP8.5).

Key words and phrases: Global climate data, High-dimensional functional data, Two-sample test, Mean function, Multi-resolution projection

Information

Preprint No.SS-2025-0356
Manuscript IDSS-2025-0356
Complete AuthorsShouxia Wang, Jiguo Cao, Hua Liu, Jinhong You, Jicai Liu
Corresponding AuthorsJicai Liu
Emailsliujicai1234@126.com

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Acknowledgments

Shouxia Wang’s research was supported by National Natural Science Foundation of China (NSFC) (No.72501165).

Jiguo Cao’s research was supported by Natural Sciences and Engineering Research Council of Canada

Discovery grant (RGPIN-2023-04057). Hua Liu’s research was supported

by the NSFC (No.12201487). Jinhong You’s research was supported by the

111-Center Project of China (No. B25066). The corresponding authors are

Jicai Liu and Jinhong You (co-corresponding).

Supplementary Materials

We provide additional simulation and real data analysis results, and technical details in the Supplementary Material.

Supplementary materials are available for download.