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A History of the Delta Method and Some New Results

Author

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  • Anil K. Bera

    (Department of Economics University of Illinois at Urbana-Champaign)

  • Malabika Koley

    (Department of Economics University of Illinois at Urbana-Champaign)

Abstract

Use of the delta method in statistics and econometrics is ubiquitous. Its mention can be found in almost all advanced statistics and econometrics textbooks but mostly without any reference. It appears that nobody knows for certain when the first paper on the topic was published or how the idea was first conceived. A seemingly unrelated method to find the asymptotic variance of a statistic involving one or more nuisance parameters was given by Pierce (Ann. Stat 10, 475–478 1982). In the first part of the paper a comprehensive review of the delta method is presented with the objective of unearthing its history. In the second part a comparative analytic study of the delta method with the Pierce method is presented.

Suggested Citation

  • Anil K. Bera & Malabika Koley, 2023. "A History of the Delta Method and Some New Results," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(2), pages 272-306, November.
    • Handle: RePEc:spr:sankhb:v:85:y:2023:i:2:d:10.1007_s13571-023-00305-9
    DOI: 10.1007/s13571-023-00305-9
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    1. Vella, Francis & Verbeek, Marno, 1999. "Two-step estimation of panel data models with censored endogenous variables and selection bias," Journal of Econometrics, Elsevier, vol. 90(2), pages 239-263, June.
    2. Prakash Gorroochurn, 2020. "Who Invented the Delta Method, Really?," The Mathematical Intelligencer, Springer, vol. 42(3), pages 46-49, September.
    3. Hong, Han & Li, Jessie, 2018. "The numerical delta method," Journal of Econometrics, Elsevier, vol. 206(2), pages 379-394.
    4. Durbin, J, 1970. "Testing for Serial Correlation in Least-Squares Regression When Some of the Regressors are Lagged Dependent Variables," Econometrica, Econometric Society, vol. 38(3), pages 410-421, May.
    5. Beutner, Eric & Zähle, Henryk, 2010. "A modified functional delta method and its application to the estimation of risk functionals," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2452-2463, November.
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    Cited by:

    1. Logachov, A. & Yambartsev, A., 2025. "The law of the iterated logarithm for functionals of the Wiener process," Statistics & Probability Letters, Elsevier, vol. 219(C).

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