Victor Chernozhukov, Christian Hansen, Yuan Liao, Yinchu Zhu
arXiv 6 Jul 2021 · Mathematics — Statistics Theory · publishedThe Annals of Statistics (2023) · 26 citations (OpenAlex)
arXiv:2107.02602 · PDF · DOI · OpenAlex · Extracted main text
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.
appendix boundary found by none_found · 100% of the source is main text. Read the extracted text to check this.
The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Chen, Y., Fan, J., Ma, C. and Yan, Y (2019) Inference and uncertainty quantification for noisy matrix completion | 0.811 | 4 | 2 | 100% |
| 2 | Chernozhukov, V., Hansen, C., Liao, Y. and Zhu, Y (2018) Inference for heterogeneous effects using low-rank estimations self | 0.811 | 4 | 2 | 100% |
| 3 | Jankova, J. and Van De Geer, S (2018) Semiparametric efficiency bounds for high-dimensional models | 0.811 | 4 | 2 | 100% |
| 4 | Keshavan, R. H., Montanari, A. and Oh, S (2010) Matrix completion from a few entries | 0.737 | 3 | 2 | 100% |
| 5 | Koltchinskii, V., Lounici, K. and Tsybakov, A. B (2011) Nuclear-norm penalization and optimal rates for noisy low-rank matrix completion | 0.737 | 3 | 2 | 100% |
| 6 | Belloni, A. and Chernozhukov, V (2013) Least squares after model selection in high-dimensional sparse models self | 0.644 | 2 | 2 | 100% |
| 7 | Hastie, T., Mazumder, R., Lee, J. D. and Zadeh, R (2015) Matrix completion and low-rank svd via fast alternating least squares | 0.644 | 2 | 2 | 100% |
| 8 | Negahban, S. and Wainwright, M. J (2011) Estimation of (near) low-rank matrices with noise and high-dimensional scaling | 0.644 | 2 | 2 | 100% |
| 9 | Zhu, Z., Wang, T. and Samworth, R. J (2019) High-dimensional principal component analysis with heterogeneous missingness | 0.644 | 2 | 2 | 100% |
| 10 | Xia, D. and Yuan, M (2019) Statistical inferences of linear forms for noisy matrix completion | 0.585 | 3 | 1 | 100% |
Showing the top 10 of 33 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.