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Inference for Low-rank Models without Estimating the Rank

Jungjun Choi, Hyukjun Kwon, Yuan Liao

arXiv 28 Nov 2023 · Econometrics · publishedJournal of the American Statistical Association (2025)

arXiv:2311.16440 · PDF · DOI · OpenAlex · Extracted main text

Abstract

This paper studies the inference about linear functionals of high-dimensional low-rank matrices. While most existing inference methods would require consistent estimation of the true rank, our procedure is robust to rank misspecification, making it a promising approach in applications where rank estimation can be unreliable. We estimate the low-rank spaces using pre-specified weighting matrices, known as diversified projections. A novel statistical insight is that, unlike the usual statistical wisdom that overfitting mainly introduces additional variances, the over-estimated low-rank space also gives rise to a non-negligible bias due to an implicit ridge-type regularization. We develop a new inference procedure and show that the central limit theorem holds as long as the pre-specified rank is no smaller than the true rank. In one of our applications, we study multiple testing with incomplete data in the presence of confounding factors and show that our method remains valid as long as the number of controlled confounding factors is at least as large as the true number, even when no confounding factors are present.

Citation extraction

43
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distinct cited
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Most heavily cited references

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.

ReferenceIntensityMentionsSectionsMain text
1Chernozhukov, V., Hansen, C., Liao, Y., and Zhu, Y (2023) Inference for low-rank models self0.92843100%
2Choi, J., Kwon, H., and Liao, Y (2023) Inference for low-rank completion without sample splitting with application to treatment effect estimation self0.92843100%
3Fan, J. and Liao, Y (2022) Learning latent factors from diversified projections and its applications to over-estimated and weak factors self0.81142100%
4Chen, Y., Fan, J., Ma, C., and Yan, Y (2019) Inference and uncertainty quantification for noisy matrix completion0.73732100%
5Chernozhukov, V., Hansen, C., Liao, Y., and Zhu, Y (2018) arXiv preprint arXiv:1812.08089 self0.73732100%
6Xia, D. and Yuan, M (2021) Statistical inferences of linear forms for noisy matrix completion0.73732100%
7Bai, J. and Ng, S (2023) Approximate factor models with weaker loadings0.64422100%
8Fan, J., Liao, Y., and Wang, W (2016) Projected principal component analysis in factor models self0.64422100%
9Onatski, A (2012) Asymptotics of the principal components estimator of large factor models with weakly influential factors0.64422100%
10Wang, J., Zhao, Q., Hastie, T., and Owen, A. B (2017) Confounder adjustment in multiple hypothesis testing0.51121100%

Showing the top 10 of 43 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
12401.136650.40511
2When can weak latent factors be statistically inferred?0.40511
3Fixed-order PCA: Theory for Overestimated Factor Models0.40511