{"title":"Large factor model estimation by nuclear norm plus ℓ1 norm penalization","authors":"Matteo Farnè, Angela Montanari","doi":"10.1016/j.jmva.2023.105244","DOIUrl":null,"url":null,"abstract":"<div><p>This paper provides a comprehensive estimation framework via nuclear norm plus <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> norm penalization for high-dimensional approximate factor models with a sparse residual covariance. The underlying assumptions allow for non-pervasive latent eigenvalues and a prominent residual covariance pattern. In that context, existing approaches based on principal components may lead to misestimate the latent rank. On the contrary, the proposed optimization strategy recovers with high probability both the covariance matrix components and the latent rank and the residual sparsity pattern. Conditioning on the recovered low rank and sparse matrix varieties, we derive the finite sample covariance matrix estimators with the tightest error bound in minimax sense and we prove that the ensuing estimators of factor loadings and scores via Bartlett’s and Thomson’s methods have the same property. The asymptotic rates for those estimators of factor loadings and scores are also provided.</p></div>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0047259X23000908/pdfft?md5=728de694d0d649b95d2f5a00e75117a5&pid=1-s2.0-S0047259X23000908-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0047259X23000908","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
This paper provides a comprehensive estimation framework via nuclear norm plus norm penalization for high-dimensional approximate factor models with a sparse residual covariance. The underlying assumptions allow for non-pervasive latent eigenvalues and a prominent residual covariance pattern. In that context, existing approaches based on principal components may lead to misestimate the latent rank. On the contrary, the proposed optimization strategy recovers with high probability both the covariance matrix components and the latent rank and the residual sparsity pattern. Conditioning on the recovered low rank and sparse matrix varieties, we derive the finite sample covariance matrix estimators with the tightest error bound in minimax sense and we prove that the ensuing estimators of factor loadings and scores via Bartlett’s and Thomson’s methods have the same property. The asymptotic rates for those estimators of factor loadings and scores are also provided.
期刊介绍:
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.