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Off-diagonal elements of projection matrices and dimension asymptotics

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  • Anatolyev, Stanislav
  • Smirnov, Maksim

Abstract

We provide insights on asymptotic behavior of the off-diagonal elements of projection matrices in settings, where the dimension of underlying vectors grows with the sample size. Under designs favorable to application of the random matrix theory, the off-diagonal elements are asymptotically normal with a simple variance expression. We also discuss the robustness of the result to deviations of the design from the ideal setup.

Suggested Citation

  • Anatolyev, Stanislav & Smirnov, Maksim, 2024. "Off-diagonal elements of projection matrices and dimension asymptotics," Economics Letters, Elsevier, vol. 239(C).
    • Handle: RePEc:eee:ecolet:v:239:y:2024:i:c:s0165176524002453
    DOI: 10.1016/j.econlet.2024.111761
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    References listed on IDEAS

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    1. Paul A. Bekker & Jan van der Ploeg, 2005. "Instrumental variable estimation based on grouped data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 59(3), pages 239-267, August.
    2. Matias D. Cattaneo & Michael Jansson & Whitney K. Newey, 2018. "Inference in Linear Regression Models with Many Covariates and Heteroscedasticity," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(523), pages 1350-1361, July.
    3. Chao, John C. & Swanson, Norman R. & Hausman, Jerry A. & Newey, Whitney K. & Woutersen, Tiemen, 2012. "Asymptotic Distribution Of Jive In A Heteroskedastic Iv Regression With Many Instruments," Econometric Theory, Cambridge University Press, vol. 28(1), pages 42-86, February.
    4. Anatolyev, Stanislav & Yaskov, Pavel, 2017. "Asymptotics Of Diagonal Elements Of Projection Matrices Under Many Instruments/Regressors," Econometric Theory, Cambridge University Press, vol. 33(3), pages 717-738, June.
    5. Hasselt, Martijn van, 2010. "Many Instruments Asymptotic Approximations Under Nonnormal Error Distributions," Econometric Theory, Cambridge University Press, vol. 26(2), pages 633-645, April.
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    More about this item

    Keywords

    Projection matrix; Many instruments/regressors; Dimension asymptotics;
    All these keywords.

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions

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