{"title":"High-dimensional rank-based graphical models for non-Gaussian functional data","authors":"Eftychia Solea, Rayan Al Hajj","doi":"10.1080/02331888.2023.2201009","DOIUrl":null,"url":null,"abstract":"We study high-dimensional graphical models for non-Gaussian functional data. To relax the Gaussian assumption, we consider the functional Gaussian copula graphical model proposed by Solea and Li [Copula Gaussian graphical models for functional data. J Am Stat Assoc. 2022;117(538):781–793]. To estimate robustly the conditional independence relationships among the functions, we propose a new rank-based correlation operator, the Kendall's tau correlation operator that extends the Kendall's tau correlation matrix at the functional setting. We establish new concentration inequalities and bounds of the rank-based estimator, which guarantee graph estimation consistency. We consider both completely and partially observed functional data, while allowing the graph size to grow with the sample size and accounting for the errors in the estimated functional principal components scores. We illustrate the finite sample properties of our method through simulation studies and a brain data set collected from functional magnetic resonance imaging for ADHD subjects.","PeriodicalId":54358,"journal":{"name":"Statistics","volume":"41 1","pages":"388 - 422"},"PeriodicalIF":1.2000,"publicationDate":"2023-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Statistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/02331888.2023.2201009","RegionNum":4,"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
We study high-dimensional graphical models for non-Gaussian functional data. To relax the Gaussian assumption, we consider the functional Gaussian copula graphical model proposed by Solea and Li [Copula Gaussian graphical models for functional data. J Am Stat Assoc. 2022;117(538):781–793]. To estimate robustly the conditional independence relationships among the functions, we propose a new rank-based correlation operator, the Kendall's tau correlation operator that extends the Kendall's tau correlation matrix at the functional setting. We establish new concentration inequalities and bounds of the rank-based estimator, which guarantee graph estimation consistency. We consider both completely and partially observed functional data, while allowing the graph size to grow with the sample size and accounting for the errors in the estimated functional principal components scores. We illustrate the finite sample properties of our method through simulation studies and a brain data set collected from functional magnetic resonance imaging for ADHD subjects.
期刊介绍:
Statistics publishes papers developing and analysing new methods for any active field of statistics, motivated by real-life problems. Papers submitted for consideration should provide interesting and novel contributions to statistical theory and its applications with rigorous mathematical results and proofs. Moreover, numerical simulations and application to real data sets can improve the quality of papers, and should be included where appropriate. Statistics does not publish papers which represent mere application of existing procedures to case studies, and papers are required to contain methodological or theoretical innovation. Topics of interest include, for example, nonparametric statistics, time series, analysis of topological or functional data. Furthermore the journal also welcomes submissions in the field of theoretical econometrics and its links to mathematical statistics.