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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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    1. Dmitry Arkhangelsky & Susan Athey & David A. Hirshberg & Guido W. Imbens & Stefan Wager, 2021. "Synthetic Difference-in-Differences," American Economic Review, American Economic Association, vol. 111(12), pages 4088-4118, December.
    2. Jushan Bai & Serena Ng, 2021. "Matrix Completion, Counterfactuals, and Factor Analysis of Missing Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1746-1763, October.
    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.
    4. Anderson, Gary M & Tollison, Robert D, 1991. "Congressional Influence and Patterns of New Deal Spending, 1933-1939," Journal of Law and Economics, University of Chicago Press, vol. 34(1), pages 161-175, April.
    5. Jin, Sainan & Miao, Ke & Su, Liangjun, 2021. "On factor models with random missing: EM estimation, inference, and cross validation," Journal of Econometrics, Elsevier, vol. 222(1), pages 745-777.
    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.
    8. Berry, Christopher R. & Burden, Barry C. & Howell, William G., 2010. "The President and the Distribution of Federal Spending," American Political Science Review, Cambridge University Press, vol. 104(4), pages 783-799, November.
    9. 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.
    10. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881.
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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.

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