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Likelihood for statistically equivalent models

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  • John Copas
  • Shinto Eguchi

Abstract

Summary. In likelihood inference we usually assume that the model is fixed and then base inference on the corresponding likelihood function. Often, however, the choice of model is rather arbitrary, and there may be other models which fit the data equally well. We study robustness of likelihood inference over such ‘statistically equivalent’ models and suggest a simple ‘envelope likelihood’ to capture this aspect of model uncertainty. Robustness depends critically on how we specify the parameter of interest. Some asymptotic theory is presented, illustrated by three examples.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jorssb:v:72:y:2010:i:2:p:193-217
    DOI: 10.1111/j.1467-9868.2009.00732.x
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    References listed on IDEAS

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    1. Richard Royall & Tsung‐Shan Tsou, 2003. "Interpreting statistical evidence by using imperfect models: robust adjusted likelihood functions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 391-404, May.
    2. 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.
    3. John Copas & Shinto Eguchi, 2005. "Local model uncertainty and incomplete‐data bias (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(4), pages 459-513, September.
    4. Masayuki Henmi & Shinto Eguchi, 2004. "A paradox concerning nuisance parameters and projected estimating functions," Biometrika, Biometrika Trust, vol. 91(4), pages 929-941, December.
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    Cited by:

    1. Masataka Taguri, 2022. "Discussion of “Akaike Memorial Lecture 2020: Some of the challenges of statistical applications”," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(4), pages 643-647, August.
    2. John Copas, 2022. "Akaike Memorial Lecture 2020: Some of the challenges of statistical applications," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(4), pages 615-637, August.
    3. Jim Smith & Fabio Rigat, 2012. "Isoseparation and robustness in parametric Bayesian inference," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(3), pages 495-519, June.

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