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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 $\Pi_0$. A defining feature of our setup is the null hypothesis of the form $\mathrm H_0: \mathrm{rank}(\Pi_0)\le r$. The problem is of first order importance because the previous literature focuses on $\mathrm H_0': \mathrm{rank}(\Pi_0)= r$ by implicitly assuming away $\mathrm{rank}(\Pi_0)

Suggested Citation

  • Qihui Chen & Zheng Fang, 2018. "Improved Inference on the Rank of a Matrix," Papers 1812.02337, arXiv.org, revised Mar 2019.
    • Handle: RePEc:arx:papers:1812.02337
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    6. 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.
    7. Qihui Chen & Zheng Fang & Xun Huang, 2021. "Implementing an Improved Test of Matrix Rank in Stata," Papers 2108.00511, arXiv.org.
    8. 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.
    9. Yoon, Jangsu, 2024. "Identification and estimation of sequential games of incomplete information with multiple equilibria," Journal of Econometrics, Elsevier, vol. 238(2).
    10. Brendan K. Beare & Jackson D. Clarke, 2022. "Modified Wilcoxon-Mann-Whitney tests of stochastic dominance," Papers 2210.08892, arXiv.org.
    11. 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.
    12. Wenjie Wang & Yichong Zhang, 2021. "Wild Bootstrap for Instrumental Variables Regressions with Weak and Few Clusters," Papers 2108.13707, arXiv.org, revised Jan 2024.
    13. Chen, Qihui & Fang, Zheng, 2019. "Inference on functionals under first order degeneracy," Journal of Econometrics, Elsevier, vol. 210(2), pages 459-481.
    14. Windmeijer, Frank, 2024. "Testing underidentification in linear models, with applications to dynamic panel and asset pricing models," Journal of Econometrics, Elsevier, vol. 240(2).
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