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Probability matching property of adjusted likelihoods

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  • Chang, In Hong
  • Mukerjee, Rahul

Abstract

For models characterized by a scalar parameter, it is well known that Jeffrey's prior ensures approximate frequentist validity of posterior quantiles. We examine how far this result remains robust in the presence of nuisance parameters, when the interest parameter [theta]1 is scalar, a prior on [theta]1 alone is considered, and the analysis is based on an adjusted version of the profile likelihood, rather than the true likelihood. This provides justification, from a Bayesian viewpoint, for some popular adjustments in term of their ability to neutralize unknown nuisance parameters. The dual problem of identifying adjustments that make a given prior on [theta]1 probability matching in the above sense is also addressed.

Suggested Citation

  • Chang, In Hong & Mukerjee, Rahul, 2006. "Probability matching property of adjusted likelihoods," Statistics & Probability Letters, Elsevier, vol. 76(8), pages 838-842, April.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:8:p:838-842
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    References listed on IDEAS

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    1. Gauri S. Datta & Thomas J. DiCiccio, 2001. "On expected volumes of multidimensional confidence sets associated with the usual and adjusted likelihoods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(4), pages 691-703.
    2. R. Mukerjee & N. Reid, 1999. "On confidence intervals associated with the usual and adjusted likelihoods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(4), pages 945-953.
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    Cited by:

    1. Ventura, Laura & Racugno, Walter, 2012. "On interval and point estimators based on a penalization of the modified profile likelihood," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1285-1289.
    2. Chang, In Hong & Mukerjee, Rahul, 2010. "Highest posterior density regions with approximate frequentist validity: The role of data-dependent priors," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1791-1797, December.
    3. Ventura, Laura & Cabras, Stefano & Racugno, Walter, 2009. "Prior Distributions From Pseudo-Likelihoods in the Presence of Nuisance Parameters," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 768-774.

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