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Uniformity and the Delta Method

Author

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  • Kasy Maximilian

    (Department of Economics, Harvard University, Littauer Center 200, 1805 Cambridge Street, Cambridge, MA 02138, USA)

Abstract

When are asymptotic approximations using the delta-method uniformly valid? We provide sufficient conditions as well as closely related necessary conditions for uniform negligibility of the remainder of such approximations. These conditions are easily verified by empirical practitioners and permit to identify settings and parameter regions where pointwise asymptotic approximations perform poorly. Our framework allows for a unified and transparent discussion of uniformity issues in various sub-fields of statistics and econometrics. Our conditions involve uniform bounds on the remainder of a first-order approximation for the function of interest.

Suggested Citation

  • Kasy Maximilian, 2019. "Uniformity and the Delta Method," Journal of Econometric Methods, De Gruyter, vol. 8(1), pages 1-19, January.
    • Handle: RePEc:bpj:jecome:v:8:y:2019:i:1:p:19:n:9
    DOI: 10.1515/jem-2018-0001
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    References listed on IDEAS

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    1. Alexandre Belloni & Victor Chernozhukov & Ivan Fernandez-Val & Christian Hansen, 2013. "Program evaluation with high-dimensional data," CeMMAP working papers 77/13, Institute for Fiscal Studies.
    2. Peter C. B. Phillips, 2012. "Folklore Theorems, Implicit Maps, and Indirect Inference," Econometrica, Econometric Society, vol. 80(1), pages 425-454, January.
    3. Leeb, Hannes & Pötscher, Benedikt M., 2005. "Model Selection And Inference: Facts And Fiction," Econometric Theory, Cambridge University Press, vol. 21(1), pages 21-59, February.
    4. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, July.
    5. Donald W. K. Andrews & Marcelo J. Moreira & James H. Stock, 2006. "Optimal Two-Sided Invariant Similar Tests for Instrumental Variables Regression," Econometrica, Econometric Society, vol. 74(3), pages 715-752, May.
    6. Guggenberger, Patrik, 2010. "The Impact Of A Hausman Pretest On The Asymptotic Size Of A Hypothesis Test," Econometric Theory, Cambridge University Press, vol. 26(2), pages 369-382, April.
    7. Anna Mikusheva, 2007. "Uniform Inference in Autoregressive Models," Econometrica, Econometric Society, vol. 75(5), pages 1411-1452, September.
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    Cited by:

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    2. Alexis Derumigny & Lucas Girard & Yannick Guyonvarch, 2025. "Can we have it all? Non-asymptotically valid and asymptotically exact confidence intervals for expectations and linear regressions," Papers 2507.16776, arXiv.org, revised Jul 2025.
    3. Inoue, Atsushi & Kilian, Lutz, 2020. "The uniform validity of impulse response inference in autoregressions," Journal of Econometrics, Elsevier, vol. 215(2), pages 450-472.
    4. JoonHwan Cho & Thomas M. Russell, 2018. "Simple Inference on Functionals of Set-Identified Parameters Defined by Linear Moments," Papers 1810.03180, arXiv.org, revised May 2023.
    5. Holberg, Christian & Ditlevsen, Susanne, 2025. "Uniform inference for cointegrated vector autoregressive processes," Journal of Econometrics, Elsevier, vol. 247(C).
    6. Baillien, Jonas & Gijbels, Irène & Verhasselt, Anneleen, 2023. "A new distance based measure of asymmetry," Journal of Multivariate Analysis, Elsevier, vol. 193(C).

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