Journal article
INFERENCE FOR LOW-RANK MODELS
The Annals of statistics, Vol.51(3), pp.1309-1330
06/01/2023
DOI: 10.1214/23-AOS2293
Abstract
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.
Details
- Title: Subtitle
- INFERENCE FOR LOW-RANK MODELS
- Creators
- Victor Chernozhukov - Massachusetts Institute of TechnologyChristian Hansen - University of ChicagoYuan Liao - Rutgers, The State University of New JerseyYinchu Zhu - Brandeis University
- Resource Type
- Journal article
- Publication Details
- The Annals of statistics, Vol.51(3), pp.1309-1330
- DOI
- 10.1214/23-AOS2293
- ISSN
- 0090-5364
- eISSN
- 2168-8966
- Publisher
- INST MATHEMATICAL STATISTICS-IMS
- Number of pages
- 22
- Language
- English
- Date published
- 06/01/2023
- Academic Unit
- Economics
- Record Identifier
- 9984936835902771
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