{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,13]],"date-time":"2026-09-13T00:07:26Z","timestamp":1789258046504,"version":"build-2803163510"},"reference-count":29,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,7,6]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>We consider the problem of identifying the pattern of latent variables in high-dimensional linear latent variable models, which can also be interpreted as determining the source of spiked singular values in the data matrix. Specifically, we test whether the latent variables are continuous or categorical, a distinction that is crucial for data interpretation, but challenging in the high-dimensional regime. To address this inference problem, we analyse the asymptotic behaviour of empirical measures associated with singular vectors corresponding to large spiked singular values. Leveraging these insights, we propose novel test statistics based on eigenvector quantile differences and establish their theoretical performance under the null hypothesis. Simulation studies and real-data analyses demonstrate the effectiveness and practical utility of our method.<\/jats:p>","DOI":"10.1093\/biomet\/asag044","type":"journal-article","created":{"date-parts":[[2026,6,29]],"date-time":"2026-06-29T16:42:41Z","timestamp":1782751361000},"source":"Crossref","is-referenced-by-count":0,"title":["Identifying the source of spikes: factor or mixture?"],"prefix":"10.1093","volume":"113","author":[{"given":"Zeqin","family":"Lin","sequence":"first","affiliation":[{"name":"School of Physical and Mathematical Sciences, Nanyang Technological University , 21 Nanyang Link , Singapore 637332, \u00a0 zeqin.lin@ntu.edu.sg","place":["Singapore"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9997-5312","authenticated-orcid":false,"given":"Yiming","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Economics, Jinan University , No. 601 Huangpu Avenue West , Guangzhou 510632,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guangming","family":"Pan","sequence":"additional","affiliation":[{"name":"School of Physical and Mathematical Sciences, Nanyang Technological University , 21 Nanyang Link , 637332, \u00a0 gmpan@ntu.edu.sg","place":["Singapore Singapore"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chi","family":"Yao","sequence":"additional","affiliation":[{"name":"School of Big Data and Statistics, Anhui University , No. 111 Jiulong Road , Hefei 230601, \u00a0 yaochi_yckey@163.com","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jia","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Economics, Hefei University of Technology , No. 485 Danxia Road , Hefei 230601, \u00a0 2023800034@hfut.edu.cn","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2026,6,29]]},"reference":[{"key":"2026091219262891100_asag044-B1","doi-asserted-by":"crossref","first-page":"1203","DOI":"10.3982\/ECTA8968","article-title":"Eigenvalue ratio test for the number of factors","volume":"81","author":"Ahn","year":"2013","journal-title":"Econometrica"},{"key":"2026091219262891100_asag044-B2","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1016\/j.jmva.2011.10.009","article-title":"On sample eigenvalues in a generalized spiked population model","volume":"106","author":"Bai","year":"2012","journal-title":"J. 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