{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,17]],"date-time":"2026-08-17T20:46:28Z","timestamp":1786999588436,"version":"build-2736575974"},"reference-count":37,"publisher":"Cambridge University Press (CUP)","license":[{"start":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T00:00:00Z","timestamp":1768348800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"abstract":"<jats:p>\n                    This article studies the principal component analysis (PCA) estimation of weak factor models with sparse loadings. We uncover an intrinsic\n                    <jats:italic>near-sparsity preservation<\/jats:italic>\n                    property for the PCA estimators of loadings, which comes from the approximately (block)\n                    <jats:italic>upper triangular<\/jats:italic>\n                    structure of the rotation matrix. It suggests an asymmetric relationship among factors: the sparsity of the rotated loadings for a stronger factor can be contaminated by the loadings from weaker ones, but the sparsity of the rotated loadings of a weaker factor is almost unaffected by the loadings of stronger ones. Then, we propose a simple alternative to the existing penalized approaches to sparsify the loading estimators by screening out the small PCA loading estimators directly, and construct consistent estimators for factor strengths. The proposed estimators perform well in finite samples, as shown by a set of Monte Carlo simulations.\n                  <\/jats:p>","DOI":"10.1017\/s0266466625100303","type":"journal-article","created":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T10:01:46Z","timestamp":1768384906000},"page":"1-24","source":"Crossref","is-referenced-by-count":1,"title":["CAN PRINCIPAL COMPONENT ANALYSIS PRESERVE THE SPARSITY IN FACTOR LOADINGS?"],"prefix":"10.1017","author":[{"given":"Jie","family":"Wei","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00p991c53","id-type":"ROR","asserted-by":"publisher"}],"name":"Huazhong University of Science and Technology"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yonghui","family":"Zhang","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/041pakw92","id-type":"ROR","asserted-by":"publisher"}],"name":"Renmin University of China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2026,1,14]]},"reference":[{"key":"S0266466625100303_r25","doi-asserted-by":"crossref","unstructured":"Giglio, S. , Xiu, D. , & Zhang, D. (2023). Prediction when factors are weak, Working Paper, NBER.10.2139\/ssrn.4406027","DOI":"10.2139\/ssrn.4397485"},{"key":"S0266466625100303_r38","doi-asserted-by":"publisher","DOI":"10.1080\/07350015.2021.1961786"},{"key":"S0266466625100303_r5","doi-asserted-by":"publisher","DOI":"10.1111\/1468-0262.00392"},{"key":"S0266466625100303_r23","unstructured":"Freyaldenhoven, S. (2023). Identification through sparsity in factor models: The ${\\ell}_1$ -rotation criterion. Working Paper, Federal Reserve Bank of Philadelphia."},{"key":"S0266466625100303_r26","doi-asserted-by":"publisher","DOI":"10.1111\/jofi.13415"},{"key":"S0266466625100303_r14","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2021.09.008"},{"key":"S0266466625100303_r17","doi-asserted-by":"publisher","DOI":"10.1002\/jae.2967"},{"key":"S0266466625100303_r30","doi-asserted-by":"crossref","unstructured":"Kim, S. , Raponi, V. , & Zaffaroni, P. (2024). Testing for weak factors in asset pricing, Working Paper, Imperial College Business School.10.2139\/ssrn.4819759","DOI":"10.2139\/ssrn.4819759"},{"key":"S0266466625100303_r24","doi-asserted-by":"publisher","DOI":"10.1086\/714090"},{"key":"S0266466625100303_r20","doi-asserted-by":"publisher","DOI":"10.1214\/11-AOS944"},{"key":"S0266466625100303_r29","doi-asserted-by":"crossref","unstructured":"Jiang, P. , Uematsu, Y. , & Yamagata, T. (2024). Revisiting asymptotic theory for principal component estimators of approximate factor models, Working Paper, Hitotsubashi University.10.2139\/ssrn.5056275","DOI":"10.2139\/ssrn.5056275"},{"key":"S0266466625100303_r16","unstructured":"Dello-Preite, M. , Uppal, R. , Zaffaroni, P. , & Zviadadze, I. (2024). Cross-sectional asset pricing with unsystematic risk. Working Paper, Imperial College London."},{"key":"S0266466625100303_r32","doi-asserted-by":"publisher","DOI":"10.1093\/rfs\/hhp081"},{"key":"S0266466625100303_r40","doi-asserted-by":"publisher","DOI":"10.1198\/073500102317351921"},{"key":"S0266466625100303_r34","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2020.07.003"},{"key":"S0266466625100303_r6","doi-asserted-by":"crossref","first-page":"1229","DOI":"10.3982\/ECTA6135","article-title":"Panel data models with interactive fixed effects","volume":"77","author":"Bai","year":"2009","journal-title":"Econometrica"},{"key":"S0266466625100303_r3","article-title":"Robust estimation and inference in panels with interactive fixed effects","author":"Armstrong","year":"2025","journal-title":"Journal of Political Economy"},{"key":"S0266466625100303_r35","doi-asserted-by":"publisher","DOI":"10.1162\/REST_a_00043"},{"key":"S0266466625100303_r43","doi-asserted-by":"publisher","DOI":"10.1080\/07350015.2021.2008405"},{"key":"S0266466625100303_r11","doi-asserted-by":"publisher","DOI":"10.1002\/jae.2830"},{"key":"S0266466625100303_r4","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2016.1195743"},{"key":"S0266466625100303_r31","doi-asserted-by":"publisher","DOI":"10.1080\/07350015.2015.1084308"},{"key":"S0266466625100303_r12","doi-asserted-by":"publisher","DOI":"10.64202\/wp.134.202205"},{"key":"S0266466625100303_r2","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":"S0266466625100303_r19","doi-asserted-by":"publisher","DOI":"10.1016\/0304-405X(93)90023-5"},{"key":"S0266466625100303_r22","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2021.04.006"},{"key":"S0266466625100303_r10","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2023.01.027"},{"key":"S0266466625100303_r41","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466613000017"},{"key":"S0266466625100303_r9","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2019.04.021"},{"key":"S0266466625100303_r36","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2012.01.034"},{"key":"S0266466625100303_r42","doi-asserted-by":"publisher","DOI":"10.1080\/07350015.2021.2003203"},{"key":"S0266466625100303_r7","doi-asserted-by":"publisher","DOI":"10.1111\/1468-0262.00273"},{"key":"S0266466625100303_r13","doi-asserted-by":"crossref","unstructured":"Chao, J. 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Selecting the relevant variables for factor estimation in FAVAR models, Working Paper, Maryland University.10.2139\/ssrn.4308280","DOI":"10.2139\/ssrn.4308280"},{"key":"S0266466625100303_r15","doi-asserted-by":"publisher","DOI":"10.1111\/j.1540-6261.2011.01671.x"},{"key":"S0266466625100303_r1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511810800"},{"key":"S0266466625100303_r21","doi-asserted-by":"publisher","DOI":"10.3982\/ECTA12749"},{"key":"S0266466625100303_r27","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2022.03.005"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466625100303","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T10:01:52Z","timestamp":1768384912000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466625100303\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,14]]},"references-count":37,"alternative-id":["S0266466625100303"],"URL":"https:\/\/doi.org\/10.1017\/s0266466625100303","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1,14]]}}}