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Entrywise Inference for Missing Panel Data: A Simple and Instance-Optimal Approach

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  • Yuling Yan
  • Martin J. Wainwright

Abstract

Longitudinal or panel data can be represented as a matrix with rows indexed by units and columns indexed by time. We consider inferential questions associated with the missing data version of panel data induced by staggered adoption. We propose a computationally efficient procedure for estimation, involving only simple matrix algebra and singular value decomposition, and prove non-asymptotic and high-probability bounds on its error in estimating each missing entry. By controlling proximity to a suitably scaled Gaussian variable, we develop and analyze a data-driven procedure for constructing entrywise confidence intervals with pre-specified coverage. Despite its simplicity, our procedure turns out to be instance-optimal: we prove that the width of our confidence intervals match a non-asymptotic instance-wise lower bound derived via a Bayesian Cram\'{e}r-Rao argument. We illustrate the sharpness of our theoretical characterization on a variety of numerical examples. Our analysis is based on a general inferential toolbox for SVD-based algorithm applied to the matrix denoising model, which might be of independent interest.

Suggested Citation

  • Yuling Yan & Martin J. Wainwright, 2024. "Entrywise Inference for Missing Panel Data: A Simple and Instance-Optimal Approach," Papers 2401.13665, arXiv.org, revised Jul 2024.
    • Handle: RePEc:arx:papers:2401.13665
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    References listed on IDEAS

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    1. Azeem M. Shaikh & Panos Toulis, 2021. "Randomization Tests in Observational Studies With Staggered Adoption of Treatment," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1835-1848, October.
    2. Susan Athey & Mohsen Bayati & Nikolay Doudchenko & Guido Imbens & Khashayar Khosravi, 2021. "Matrix Completion Methods for Causal Panel Data Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1716-1730, October.
    3. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881, November.
    4. 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.
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    Cited by:

    1. Guanhao Zhou & Yuefeng Han & Xiufan Yu, 2025. "Covariate-Adjusted Deep Causal Learning for Heterogeneous Panel Data Models," Papers 2505.20536, arXiv.org.

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