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Statistical inferences of linear forms for noisy matrix completion

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  • Dong Xia
  • Ming Yuan

Abstract

We introduce a flexible framework for making inferences about general linear forms of a large matrix based on noisy observations of a subset of its entries. In particular, under mild regularity conditions, we develop a universal procedure to construct asymptotically normal estimators of its linear forms through double‐sample debiasing and low‐rank projection whenever an entry‐wise consistent estimator of the matrix is available. These estimators allow us to subsequently construct confidence intervals for and test hypotheses about the linear forms. Our proposal was motivated by a careful perturbation analysis of the empirical singular spaces under the noisy matrix completion model which might be of independent interest. The practical merits of our proposed inference procedure are demonstrated on both simulated and real‐world data examples.

Suggested Citation

  • Dong Xia & Ming Yuan, 2021. "Statistical inferences of linear forms for noisy matrix completion," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(1), pages 58-77, February.
    • Handle: RePEc:bla:jorssb:v:83:y:2021:i:1:p:58-77
    DOI: 10.1111/rssb.12400
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    References listed on IDEAS

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    1. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2018. "Double/debiased machine learning for treatment and structural parameters," Econometrics Journal, Royal Economic Society, vol. 21(1), pages 1-68, February.
    2. Tianxi Cai & T. Tony Cai & Anru Zhang, 2016. "Structured Matrix Completion with Applications to Genomic Data Integration," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 621-633, April.
    3. Minsker, Stanislav, 2017. "On some extensions of Bernstein’s inequality for self-adjoint operators," Statistics & Probability Letters, Elsevier, vol. 127(C), pages 111-119.
    4. Cun-Hui Zhang & Stephanie S. Zhang, 2014. "Confidence intervals for low dimensional parameters in high dimensional linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(1), pages 217-242, January.
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    Cited by:

    1. Choi, Jungjun & Kwon, Hyukjun & Liao, Yuan, 2024. "Inference for low-rank completion without sample splitting with application to treatment effect estimation," Journal of Econometrics, Elsevier, vol. 240(1).
    2. Jianqing Fan & Yuling Yan & Yuheng Zheng, 2024. "When can weak latent factors be statistically inferred?," Papers 2407.03616, arXiv.org, revised Sep 2024.
    3. Jungjun Choi & Hyukjun Kwon & Yuan Liao, 2023. "Inference for Low-rank Completion without Sample Splitting with Application to Treatment Effect Estimation," Papers 2307.16370, arXiv.org.
    4. Jungjun Choi & Hyukjun Kwon & Yuan Liao, 2023. "Inference for Low-rank Models without Estimating the Rank," Papers 2311.16440, arXiv.org, revised Oct 2024.
    5. Jungjun Choi & Ming Yuan, 2023. "Matrix Completion When Missing Is Not at Random and Its Applications in Causal Panel Data Models," Papers 2308.02364, arXiv.org.

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