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Uniformity and the delta method

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  • Kasy, Maximilian

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 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 econometrics. Our conditions involve uniform bounds on the remainder of a first-order approximation for the function of interest.

Suggested Citation

  • Kasy, Maximilian, 2015. "Uniformity and the delta method," Working Paper 197561, Harvard University OpenScholar.
    • Handle: RePEc:qsh:wpaper:197561
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    File URL: http://scholar.harvard.edu/kasy/node/197561
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    Cited by:

    1. Antoine, Bertille & Lavergne, Pascal, 2023. "Identification-robust nonparametric inference in a linear IV model," Journal of Econometrics, Elsevier, vol. 235(1), pages 1-24.
    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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