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Improved inference on the rank of a matrix

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  • Qihui Chen
  • Zheng Fang

Abstract

This paper develops a general framework for conducting inference on the rank of an unknown matrix Π0. A defining feature of our setup is the null hypothesis of the form H0:rank(Π0)≤r. The problem is of first‐order importance because the previous literature focuses on H0′:rank(Π0)=r by implicitly assuming away rank(Π0)

Suggested Citation

  • Qihui Chen & Zheng Fang, 2019. "Improved inference on the rank of a matrix," Quantitative Economics, Econometric Society, vol. 10(4), pages 1787-1824, November.
    • Handle: RePEc:wly:quante:v:10:y:2019:i:4:p:1787-1824
    DOI: 10.3982/QE1139
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    Cited by:

    1. Qihui Chen & Nikolai Roussanov & Xiaoliang Wang, 2021. "Semiparametric Conditional Factor Models: Estimation and Inference," Papers 2112.07121, arXiv.org, revised Sep 2023.
    2. Hongyi Jiang & Zhenting Sun & Shiyun Hu, 2023. "A Nonparametric Test of $m$th-degree Inverse Stochastic Dominance," Papers 2306.12271, arXiv.org, revised Jul 2023.
    3. Zheng Fang & Juwon Seo, 2019. "A Projection Framework for Testing Shape Restrictions That Form Convex Cones," Papers 1910.07689, arXiv.org, revised Sep 2021.
    4. Zheng Fang & Juwon Seo, 2021. "A Projection Framework for Testing Shape Restrictions That Form Convex Cones," Econometrica, Econometric Society, vol. 89(5), pages 2439-2458, September.
    5. Levon Barseghyan & Francesca Molinari, 2023. "Risk Preference Types, Limited Consideration, and Welfare," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 41(4), pages 1011-1029, October.
    6. Chen, Qihui, 2021. "Robust and optimal estimation for partially linear instrumental variables models with partial identification," Journal of Econometrics, Elsevier, vol. 221(2), pages 368-380.
    7. Wenjie Wang & Yichong Zhang, 2021. "Wild Bootstrap for Instrumental Variables Regressions with Weak and Few Clusters," Papers 2108.13707, arXiv.org, revised Jan 2024.
    8. Windmeijer, Frank, 2024. "Testing underidentification in linear models, with applications to dynamic panel and asset pricing models," Journal of Econometrics, Elsevier, vol. 240(2).
    9. Lazar, Emese & Wang, Shixuan & Xue, Xiaohan, 2023. "Loss function-based change point detection in risk measures," European Journal of Operational Research, Elsevier, vol. 310(1), pages 415-431.
    10. Wang, Wenjie & Zhang, Yichong, 2024. "Wild bootstrap inference for instrumental variables regressions with weak and few clusters," Journal of Econometrics, Elsevier, vol. 241(1).
    11. Cizek, Pavel & Sadikoglu, Serhan, 2022. "Nonseparable Panel Models with Index Structure and Correlated Random Effects," Other publications TiSEM 7899deb9-0eda-47e6-a3b8-2, Tilburg University, School of Economics and Management.
    12. Guggenberger, Patrik & Kleibergen, Frank & Mavroeidis, Sophocles, 2023. "A test for Kronecker Product Structure covariance matrix," Journal of Econometrics, Elsevier, vol. 233(1), pages 88-112.
    13. Qihui Chen & Zheng Fang & Xun Huang, 2021. "Implementing an Improved Test of Matrix Rank in Stata," Papers 2108.00511, arXiv.org.
    14. Yoon, Jangsu, 2024. "Identification and estimation of sequential games of incomplete information with multiple equilibria," Journal of Econometrics, Elsevier, vol. 238(2).
    15. Brendan K. Beare & Jackson D. Clarke, 2022. "Modified Wilcoxon-Mann-Whitney tests of stochastic dominance," Papers 2210.08892, arXiv.org.

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