{"title":"Change point analysis of functional variance function with stationary error","authors":"Qirui Hu","doi":"10.1016/j.jmva.2024.105311","DOIUrl":null,"url":null,"abstract":"<div><p>An asymptotically correct test for an abrupt break in functional variance function of measurement error in the functional sequence and the confidence interval of change point is constructed. Under general assumptions, the test and detection procedure conducted by Spline-backfitted kernel smoothing, i.e., recovering trajectories with B-spline and estimating variance function with kernel regression, enjoy oracle efficiency, namely, the proposed procedure is asymptotically indistinguishable from that with accurate trajectories. Furthermore, a consistent algorithm for multiple change points based on the binary segment is derived. Extensive simulation studies reveal a positive confirmation of the asymptotic theory. The proposed method is applied to analyze EEG data.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":null,"pages":null},"PeriodicalIF":1.4000,"publicationDate":"2024-03-11","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/S0047259X24000186","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
An asymptotically correct test for an abrupt break in functional variance function of measurement error in the functional sequence and the confidence interval of change point is constructed. Under general assumptions, the test and detection procedure conducted by Spline-backfitted kernel smoothing, i.e., recovering trajectories with B-spline and estimating variance function with kernel regression, enjoy oracle efficiency, namely, the proposed procedure is asymptotically indistinguishable from that with accurate trajectories. Furthermore, a consistent algorithm for multiple change points based on the binary segment is derived. Extensive simulation studies reveal a positive confirmation of the asymptotic theory. The proposed method is applied to analyze EEG data.
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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