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Inference for Low-rank Completion without Sample Splitting with Application to Treatment Effect Estimation

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  • Jungjun Choi
  • Hyukjun Kwon
  • Yuan Liao

Abstract

This paper studies the inferential theory for estimating low-rank matrices. It also provides an inference method for the average treatment effect as an application. We show that the least square estimation of eigenvectors following the nuclear norm penalization attains the asymptotic normality. The key contribution of our method is that it does not require sample splitting. In addition, this paper allows dependent observation patterns and heterogeneous observation probabilities. Empirically, we apply the proposed procedure to estimating the impact of the presidential vote on allocating the U.S. federal budget to the states.

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  • 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.
    • Handle: RePEc:arx:papers:2307.16370
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    References listed on IDEAS

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    3. 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.
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    6. McCarty, Nolan M., 2000. "Presidential Pork: Executive Veto Power and Distributive Politics," American Political Science Review, Cambridge University Press, vol. 94(1), pages 117-129, March.
    7. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
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    Cited by:

    1. Jungjun Choi & Hyukjun Kwon & Yuan Liao, 2023. "Inference for Low-rank Models without Estimating the Rank," Papers 2311.16440, arXiv.org, revised Oct 2024.

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