Large factor model estimation by nuclear norm plus ℓ1 norm penalization

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY
Matteo Farnè, Angela Montanari
{"title":"Large factor model estimation by nuclear norm plus ℓ1 norm penalization","authors":"Matteo Farnè,&nbsp;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 1 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.

核范数加1范数惩罚的大因子模型估计
针对残差稀疏的高维近似因子模型,提出了一种核范数加1范数惩罚的综合估计框架。基本假设允许非普遍的潜在特征值和突出的残差协方差模式。在这种情况下,现有的基于主成分的方法可能导致对潜在秩的错误估计。相反,所提出的优化策略可以高概率地恢复协方差矩阵分量以及潜在秩和残差稀疏度模式。在恢复的低秩和稀疏矩阵变异的条件下,我们导出了误差界在极小极大意义上最紧的有限样本协方差矩阵估计量,并证明了随后的因子负荷和分数的Bartlett和Thomson方法估计量具有相同的性质。对这些因子负荷和分数的估计也给出了渐近率。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
Accounts of Chemical Research
Accounts of Chemical Research 化学-化学综合
CiteScore
31.40
自引率
1.10%
发文量
312
审稿时长
2 months
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.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信