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Identification in Parametric Models: The Minimum Hellinger Distance Criterion

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  • David Pacini

    (School of Economics, University of Bristol, Bristol BS8 1TU, UK)

Abstract

This note studies the criterion for identifiability in parametric models based on the minimization of the Hellinger distance and exhibits its relationship to the identifiability criterion based on the Fisher matrix. It shows that the Hellinger distance criterion serves to establish identifiability of parameters of interest, or lack of it, in situations where the criterion based on the Fisher matrix does not apply, like in models where the support of the observed variables depends on the parameter of interest or in models with irregular points of the Fisher matrix. Several examples illustrating this result are provided.

Suggested Citation

  • David Pacini, 2022. "Identification in Parametric Models: The Minimum Hellinger Distance Criterion," Econometrics, MDPI, vol. 10(1), pages 1-14, February.
    • Handle: RePEc:gam:jecnmx:v:10:y:2022:i:1:p:10-:d:754168
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    2. P. Li & J. Chen & P. Marriott, 2009. "Non-finite Fisher information and homogeneity: an EM approach," Biometrika, Biometrika Trust, vol. 96(2), pages 411-426.
    3. Arthur Lewbel, 2019. "The Identification Zoo: Meanings of Identification in Econometrics," Journal of Economic Literature, American Economic Association, vol. 57(4), pages 835-903, December.
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    5. Bowden, Roger J, 1973. "The Theory of Parametric Identification," Econometrica, Econometric Society, vol. 41(6), pages 1069-1074, November.
    6. Rothenberg, Thomas J, 1971. "Identification in Parametric Models," Econometrica, Econometric Society, vol. 39(3), pages 577-591, May.
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    Cited by:

    1. David Pacini, 2022. "A Goodness-of-Identifiability Criterion for Parametric Statistical Models," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 11(4), pages 1-1.

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