{"title":"基于Hilbert–Schmidt独立性准则的因子模型条件独立性检验","authors":"Kai Xu , Qing Cheng","doi":"10.1016/j.jmva.2023.105241","DOIUrl":null,"url":null,"abstract":"<div><p>This work is concerned with testing conditional independence under a factor model setting. We propose a novel multivariate test for non-Gaussian data based on the Hilbert–Schmidt independence criterion (HSIC). Theoretically, we investigate the convergence of our test statistic under both the null and the alternative hypotheses, and devise a bootstrap scheme to approximate its null distribution, showing that its consistency is justified. Methodologically, we generalize the HSIC-based independence test approach to a situation where data follow a factor model structure. Our test requires no nonparametric smoothing estimation of functional forms including conditional probability density functions, conditional cumulative distribution functions and conditional characteristic functions under the null or alternative, is computationally efficient and is dimension-free in the sense that the dimension of the conditioning variable is allowed to be large but finite. Further extension to nonlinear, non-Gaussian structure equation models is also described in detail and asymptotic properties are rigorously justified. Numerical studies demonstrate the effectiveness of our proposed test relative to that of several existing tests.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":null,"pages":null},"PeriodicalIF":1.4000,"publicationDate":"2023-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Test of conditional independence in factor models via Hilbert–Schmidt independence criterion\",\"authors\":\"Kai Xu , Qing Cheng\",\"doi\":\"10.1016/j.jmva.2023.105241\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This work is concerned with testing conditional independence under a factor model setting. We propose a novel multivariate test for non-Gaussian data based on the Hilbert–Schmidt independence criterion (HSIC). Theoretically, we investigate the convergence of our test statistic under both the null and the alternative hypotheses, and devise a bootstrap scheme to approximate its null distribution, showing that its consistency is justified. Methodologically, we generalize the HSIC-based independence test approach to a situation where data follow a factor model structure. Our test requires no nonparametric smoothing estimation of functional forms including conditional probability density functions, conditional cumulative distribution functions and conditional characteristic functions under the null or alternative, is computationally efficient and is dimension-free in the sense that the dimension of the conditioning variable is allowed to be large but finite. Further extension to nonlinear, non-Gaussian structure equation models is also described in detail and asymptotic properties are rigorously justified. Numerical studies demonstrate the effectiveness of our proposed test relative to that of several existing tests.</p></div>\",\"PeriodicalId\":16431,\"journal\":{\"name\":\"Journal of Multivariate Analysis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2023-09-23\",\"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/S0047259X23000878\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Multivariate Analysis","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0047259X23000878","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
Test of conditional independence in factor models via Hilbert–Schmidt independence criterion
This work is concerned with testing conditional independence under a factor model setting. We propose a novel multivariate test for non-Gaussian data based on the Hilbert–Schmidt independence criterion (HSIC). Theoretically, we investigate the convergence of our test statistic under both the null and the alternative hypotheses, and devise a bootstrap scheme to approximate its null distribution, showing that its consistency is justified. Methodologically, we generalize the HSIC-based independence test approach to a situation where data follow a factor model structure. Our test requires no nonparametric smoothing estimation of functional forms including conditional probability density functions, conditional cumulative distribution functions and conditional characteristic functions under the null or alternative, is computationally efficient and is dimension-free in the sense that the dimension of the conditioning variable is allowed to be large but finite. Further extension to nonlinear, non-Gaussian structure equation models is also described in detail and asymptotic properties are rigorously justified. Numerical studies demonstrate the effectiveness of our proposed test relative to that of several existing 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.