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Directionally Differentiable Econometric Models

Author

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  • Cho, Jin Seo
  • White, Halbert

Abstract

The current article examines the limit distribution of the quasi-maximum likelihood estimator obtained from a directionally differentiable quasi-likelihood function and represents its limit distribution as a functional of a Gaussian stochastic process indexed by direction. In this way, the standard analysis that assumes a differentiable quasi-likelihood function is treated as a special case of our analysis. We also examine and redefine the standard quasi-likelihood ratio, Wald, and Lagrange multiplier test statistics so that their null limit behaviors are regular under our model framework.

Suggested Citation

  • Cho, Jin Seo & White, Halbert, 2018. "Directionally Differentiable Econometric Models," Econometric Theory, Cambridge University Press, vol. 34(5), pages 1101-1131, October.
    • Handle: RePEc:cup:etheor:v:34:y:2018:i:05:p:1101-1131_00
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    Cited by:

    1. Michael Jansson & Demian Pouzo, 2017. "Towards a General Large Sample Theory for Regularized Estimators," Papers 1712.07248, arXiv.org, revised Jul 2020.
    2. Jin Seo Cho & Halbert White, 2017. "Supplements to "Directionally Differentiable Econometric Models"," Working papers 2017rwp-103a, Yonsei University, Yonsei Economics Research Institute.
    3. Dakyung Seong & Jin Seo Cho & Timo Terasvirta, 2019. "Comprehensive Testing of Linearity against the Smooth Transition Autoregressive Model," Working papers 2019rwp-151, Yonsei University, Yonsei Economics Research Institute.
    4. Firpo, Sergio & Galvao, Antonio F. & Parker, Thomas, 2023. "Uniform inference for value functions," Journal of Econometrics, Elsevier, vol. 235(2), pages 1680-1699.
    5. Firpo, Sergio & Galvao, Antonio F. & Kobus, Martyna & Parker, Thomas & Rosa-Dias, Pedro, 2025. "Loss aversion and the welfare ranking of policy interventions," Journal of Econometrics, Elsevier, vol. 252(PB).
    6. David Kang & Seojeong Lee, 2025. "Misspecification-Robust Asymptotic and Bootstrap Inference for Nonsmooth GMM," Working Papers 423284005, Lancaster University Management School, Economics Department.

    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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