INFERENCE FOR LOW-RANK MODELS

• 成果类型: Article
• 署名作者: Chernozhukov, Victor; Hansen, Christian; Liao, Yuan; Zhu, Yinchu
• 署名单位: Massachusetts Institute of Technology (MIT); University of Chicago; Rutgers University System; Rutgers University New Brunswick; Brandeis University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/23-AOS2293
• 发表日期: 2023
• 页码: 1309-1330
• 关键词: matrix completion; sparse pca; Optimal Rates; selection; bounds

摘要

This paper studies inference in linear models with a high-dimensional parameter matrix that can be well approximated by a spiked low-rank matrix. A spiked low-rank matrix has rank that grows slowly compared to its dimensions and nonzero singular values that diverge to infinity. We show that this framework covers a broad class of models of latent variables, which can accommodate matrix completion problems, factor models, varying coefficient models and heterogeneous treatment effects. For inference, we apply a procedure that relies on an initial nuclear-norm penalized estimation step followed by two ordinary least squares regressions. We consider the framework of estimating incoherent eigenvectors and use a rotation argument to argue that the eigenspace estimation is asymptotically unbiased. Using this framework, we show that our procedure provides asymptotically normal inference and achieves the semiparametric efficiency bound. We illustrate our framework by providing low-level conditions for its application in a treatment effects context where treatment assignment might be strongly dependent.