{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T20:59:11Z","timestamp":1776200351335,"version":"3.50.1"},"reference-count":30,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2025,12,26]],"date-time":"2025-12-26T00:00:00Z","timestamp":1766707200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Funds of China","doi-asserted-by":"crossref","award":["12471268"],"award-info":[{"award-number":["12471268"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Funds of China","doi-asserted-by":"crossref","award":["12001517"],"award-info":[{"award-number":["12001517"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Funds of China","doi-asserted-by":"crossref","award":["72091212"],"award-info":[{"award-number":["72091212"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,4,14]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>We consider the problem of estimating the number of significant components in high-dimensional principal component analysis. We propose a new penalized approach using the explained variance ratio and the rigidity of the nonspiked sample eigenvalues of sample covariance matrices of $ p $ variables. Compared with methods in the existing literature, the consistency of the proposed estimator holds, not only for independent data, but also for some times series data when the dimension $ p $ and the sample size $ n $ both tend to infinity. Even for independent data our estimator works under weaker conditions than existing approaches such as the aic and bic, including allowing heterogeneity in the bulk of the population eigenvalues. Simulation studies are conducted to illustrate the performance of the proposed estimator.<\/jats:p>","DOI":"10.1093\/biomet\/asaf092","type":"journal-article","created":{"date-parts":[[2025,12,18]],"date-time":"2025-12-18T12:52:55Z","timestamp":1766062375000},"source":"Crossref","is-referenced-by-count":0,"title":["Estimating the number of significant components in high-dimensional principal component analysis"],"prefix":"10.1093","volume":"113","author":[{"given":"Bo","family":"Zhang","sequence":"first","affiliation":[{"name":"Department of Statistics and Finance, University of Science and Technology of China , No. 96, Jinzhai Road, Hefei 230026, \u00a0 zhangbo890301@outlook.com","place":["China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhixiang","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Macau, E11 Avenida da Universidade , Taipa, Macau 999078, \u00a0 zhixzhang@um.edu.mo","place":["China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guangming","family":"Pan","sequence":"additional","affiliation":[{"name":"School of Physical and Mathematical Sciences, Nanyang Technological University , 50 Nanyang Avenue , 639798 \u00a0 gmpan@ntu.edu.sg","place":["Singapore"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2025,12,26]]},"reference":[{"key":"2026041416014768100_asaf092-B1","doi-asserted-by":"crossref","first-page":"1050","DOI":"10.1214\/17-AOS1577","article-title":"Consistency of AIC and BIC in estimating the number of significant components in high-dimensional principal component analysis","volume":"46","author":"Bai","year":"2018","journal-title":"Ann. 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