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On measuring sensitivity to parametric model misspecification

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  • Paul Gustafson

Abstract

In settings where parametric inference is inconsistent under model misspecification, the discrepancy between correct and misspecified inferences is compared with the discrepancy between correct and misspecified models. To make the comparison tractable, large sample and small misspecification approximations are employed. The ratio of the approximate discrepancy between inferences to the approximate discrepancy between models is regarded as a relative measure of sensitivity to model misspecification. The maximum ratio over a family of correct distributions is determined as a measure of worst case sensitivity. As well, the distribution producing this maximum can be examined, to see how a particular combination of a parametric family and estimand is susceptible to model misspecifications.

Suggested Citation

  • Paul Gustafson, 2001. "On measuring sensitivity to parametric model misspecification," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(1), pages 81-94.
    • Handle: RePEc:bla:jorssb:v:63:y:2001:i:1:p:81-94
    DOI: 10.1111/1467-9868.00277
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    Cited by:

    1. Huang, Xianzheng, 2011. "Detecting random-effects model misspecification via coarsened data," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 703-714, January.
    2. Heng Chen & Daniel F. Heitjan, 2022. "Analysis of local sensitivity to nonignorability with missing outcomes and predictors," Biometrics, The International Biometric Society, vol. 78(4), pages 1342-1352, December.
    3. Paul Gustafson, 2007. "On Robustness and Model Flexibility in Survival Analysis: Transformed Hazard Models and Average Effects," Biometrics, The International Biometric Society, vol. 63(1), pages 69-77, March.
    4. Xiaoyan Shi & Hongtu Zhu & Joseph G. Ibrahim, 2009. "Local Influence for Generalized Linear Models with Missing Covariates," Biometrics, The International Biometric Society, vol. 65(4), pages 1164-1174, December.
    5. John Copas & Shinto Eguchi, 2010. "Likelihood for statistically equivalent models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(2), pages 193-217, March.
    6. Juxin Liu & Paul Gustafson, 2012. "On the detectability of different forms of interaction in regression models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(3), pages 347-365, April.

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