{"title":"A data depth based nonparametric test of independence between two random vectors","authors":"Sakineh Dehghan, Mohammad Reza Faridrohani","doi":"10.1016/j.jmva.2024.105297","DOIUrl":null,"url":null,"abstract":"<div><p>A new family of depth-based test statistics is proposed for testing the hypothesis of independence between two random vectors. In the procedure to derive the asymptotic distribution of the tests under the null hypothesis, we do not require any symmetric assumption of the distribution functions. Furthermore, a conditional distribution-free property of the tests is shown. The asymptotic relative efficiency of the tests is discussed under the class of elliptically symmetric distribution. Asymptotic relative efficiencies along with Monte Carlo results suggest that the performance of the proposed class is comparable to the existing ones, and under some circumstances, it has higher power. Finally, we apply the tests to two real data sets and also discuss the robustness of our tests.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":null,"pages":null},"PeriodicalIF":1.4000,"publicationDate":"2024-02-08","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/S0047259X24000046","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
A new family of depth-based test statistics is proposed for testing the hypothesis of independence between two random vectors. In the procedure to derive the asymptotic distribution of the tests under the null hypothesis, we do not require any symmetric assumption of the distribution functions. Furthermore, a conditional distribution-free property of the tests is shown. The asymptotic relative efficiency of the tests is discussed under the class of elliptically symmetric distribution. Asymptotic relative efficiencies along with Monte Carlo results suggest that the performance of the proposed class is comparable to the existing ones, and under some circumstances, it has higher power. Finally, we apply the tests to two real data sets and also discuss the robustness of our tests.
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.
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