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The numerical delta method

Author

Listed:
  • Hong, Han
  • Li, Jessie

Abstract

This paper provides a numerical derivative based Delta method that complements the recent work by Fang and Santos (2014) and also generalizes a previous insight by Song (2014). We show that for an appropriately chosen sequence of step sizes, the numerical derivative based Delta method provides consistent inference for functions of parameters that are only directionally differentiable. Additionally, it provides uniformly valid inference for certain convex and Lipschitz functions which include all the examples mentioned in Fang and Santos (2014). We extend our results to the second order Delta method and illustrate its applicability to inference for moment inequality models.

Suggested Citation

  • Hong, Han & Li, Jessie, 2018. "The numerical delta method," Journal of Econometrics, Elsevier, vol. 206(2), pages 379-394.
    • Handle: RePEc:eee:econom:v:206:y:2018:i:2:p:379-394
    DOI: 10.1016/j.jeconom.2018.06.007
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    References listed on IDEAS

    as
    1. Song, Kyungchul, 2014. "Local asymptotic minimax estimation of nonregular parameters with translation-scale equivariant maps," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 136-158.
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    Keywords

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    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
    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General

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