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Uniform confidence bands: Characterization and optimality

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  • Freyberger, Joachim
  • Rai, Yoshiyasu

Abstract

This paper studies optimal uniform confidence bands for functions g(x,β0), where β0 is an unknown parameter vector. We provide a simple characterization of a general class of taut 1−α uniform confidence bands, allowing for both nonlinear functions and nonparametrically estimated functions. Specifically, we show that all taut bands can be obtained from projections on confidence sets for β0 and we characterize the class of sets which yield taut bands. Using these results, we then present a computational method for selecting an approximately optimal confidence band for a given objective function. We illustrate the applicability of these results in numerical applications.

Suggested Citation

  • Freyberger, Joachim & Rai, Yoshiyasu, 2018. "Uniform confidence bands: Characterization and optimality," Journal of Econometrics, Elsevier, vol. 204(1), pages 119-130.
    • Handle: RePEc:eee:econom:v:204:y:2018:i:1:p:119-130
    DOI: 10.1016/j.jeconom.2018.01.006
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    References listed on IDEAS

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    Cited by:

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    2. Callaway, Brantly & Sant’Anna, Pedro H.C., 2021. "Difference-in-Differences with multiple time periods," Journal of Econometrics, Elsevier, vol. 225(2), pages 200-230.
    3. Montiel Olea, José Luis & Nesbit, James, 2021. "(Machine) learning parameter regions," Journal of Econometrics, Elsevier, vol. 222(1), pages 716-744.
    4. Simon Freyaldenhoven & Christian B. Hansen & Jorge Pérez Pérez & Jesse M. Shapiro & Constantino Carreto, 2024. "Policy Effect Estimation and Visualization in Linear Panel Event-Study Designs: Introducing the xtevent Package," Working Papers 2024-09, Banco de México.
    5. Simon Freyaldenhoven & Christian Hansen & Jorge Perez Perez & Jesse Shapiro, 2021. "Visualization, Identification, and stimation in the Linear Panel Event-Study Design," Working Papers 21-44, Federal Reserve Bank of Philadelphia.
    6. Constantino Carreto & Simon Freyaldenhoven & Christian Hansen & Jorge Perez Perez & Jesse Shapiro, 2024. "xtevent: Estimation and Visualization in the Linear Panel Event-Study Design," Working Papers 24-15, Federal Reserve Bank of Philadelphia.

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    More about this item

    Keywords

    Uniform confidence bands; Simultaneous inference; Projections; Optimality;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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