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Algorithmic subsampling under multiway clustering

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  • Harold D. Chiang
  • Jiatong Li
  • Yuya Sasaki

Abstract

This paper proposes a novel method of algorithmic subsampling (data sketching) for multiway cluster dependent data. We establish a new uniform weak law of large numbers and a new central limit theorem for the multiway algorithmic subsample means. Consequently, we discover an additional advantage of the algorithmic subsampling that it allows for robustness against potential degeneracy, and even non-Gaussian degeneracy, of the asymptotic distribution under multiway clustering. Simulation studies support this novel result, and demonstrate that inference with the algorithmic subsampling entails more accuracy than that without the algorithmic subsampling. Applying these basic asymptotic theories, we derive the consistency and the asymptotic normality for the multiway algorithmic subsampling generalized method of moments estimator and for the multiway algorithmic subsampling M-estimator. We illustrate an application to scanner data.

Suggested Citation

  • Harold D. Chiang & Jiatong Li & Yuya Sasaki, 2021. "Algorithmic subsampling under multiway clustering," Papers 2103.00557, arXiv.org, revised Oct 2022.
    • Handle: RePEc:arx:papers:2103.00557
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    References listed on IDEAS

    as
    1. Harold D. Chiang & Kengo Kato & Yukun Ma & Yuya Sasaki, 2022. "Multiway Cluster Robust Double/Debiased Machine Learning," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(3), pages 1046-1056, June.
    2. Djogbenou, Antoine A. & MacKinnon, James G. & Nielsen, Morten Ørregaard, 2019. "Asymptotic theory and wild bootstrap inference with clustered errors," Journal of Econometrics, Elsevier, vol. 212(2), pages 393-412.
    3. Thompson, Samuel B., 2011. "Simple formulas for standard errors that cluster by both firm and time," Journal of Financial Economics, Elsevier, vol. 99(1), pages 1-10, January.
    4. Laurent Davezies & Xavier D'Haultfoeuille & Yannick Guyonvarch, 2018. "Asymptotic results under multiway clustering," Papers 1807.07925, arXiv.org, revised Aug 2018.
    5. Harold D. Chiang & Kengo Kato & Yuya Sasaki, 2023. "Inference for High-Dimensional Exchangeable Arrays," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 118(543), pages 1595-1605, July.
    6. Serena Ng, 2017. "Opportunities and Challenges: Lessons from Analyzing Terabytes of Scanner Data," NBER Working Papers 23673, National Bureau of Economic Research, Inc.
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