{"title":"Tests for equality of several covariance matrix functions for multivariate functional data","authors":"Zhiping Qiu , Jiangyuan Fan , Jin-Ting Zhang , Jianwei Chen","doi":"10.1016/j.jmva.2023.105243","DOIUrl":null,"url":null,"abstract":"<div><p>Multivariate functional data are often observed in many scientific fields. This paper considers a multi-sample equal-covariance matrix function testing problem for multivariate functional data. Two new tests are proposed and studied. The asymptotic properties of the two tests under the null hypothesis and a local alternative are investigated. Two methods for approximating the null distributions of the test statistics are described. It is shown that the two tests are root-<span><math><mi>n</mi></math></span> consistent. Two simulation studies are conducted to evaluate the finite sample performance of the proposed tests. Finally, the two tests are illustrated via applications to three real multivariate functional data sets.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":null,"pages":null},"PeriodicalIF":1.4000,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Multivariate Analysis","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0047259X23000891","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
Multivariate functional data are often observed in many scientific fields. This paper considers a multi-sample equal-covariance matrix function testing problem for multivariate functional data. Two new tests are proposed and studied. The asymptotic properties of the two tests under the null hypothesis and a local alternative are investigated. Two methods for approximating the null distributions of the test statistics are described. It is shown that the two tests are root- consistent. Two simulation studies are conducted to evaluate the finite sample performance of the proposed tests. Finally, the two tests are illustrated via applications to three real multivariate functional data sets.
期刊介绍:
Founded in 1971, the Journal of Multivariate Analysis (JMVA) is the central venue for the publication of new, relevant methodology and particularly innovative applications pertaining to the analysis and interpretation of multidimensional data.
The journal welcomes contributions to all aspects of multivariate data analysis and modeling, including cluster analysis, discriminant analysis, factor analysis, and multidimensional continuous or discrete distribution theory. Topics of current interest include, but are not limited to, inferential aspects of
Copula modeling
Functional data analysis
Graphical modeling
High-dimensional data analysis
Image analysis
Multivariate extreme-value theory
Sparse modeling
Spatial statistics.