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On interval and point estimators based on a penalization of the modified profile likelihood

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  • Ventura, Laura
  • Racugno, Walter

Abstract

In the presence of a nuisance parameter, one widely shared approach to likelihood inference on a scalar parameter of interest is based on the profile likelihood and its various modifications. In this paper, we add a penalization to the modified profile likelihood, which is based on a suitable matching prior, and we discuss the frequency properties of interval estimators and point estimators based on this penalized modified profile likelihood. Two simulation studies are illustrated, and we indicate the improvement of the proposed penalized modified profile likelihood over its counterparts.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:7:p:1285-1289
    DOI: 10.1016/j.spl.2012.03.025
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    References listed on IDEAS

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    1. Nicole A. Lazar, 2003. "Bayesian empirical likelihood," Biometrika, Biometrika Trust, vol. 90(2), pages 319-326, June.
    2. 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.
    3. Chang, In Hong & Mukerjee, Rahul, 2006. "Probability matching property of adjusted likelihoods," Statistics & Probability Letters, Elsevier, vol. 76(8), pages 838-842, April.
    4. Thomas A. Severini, 2007. "Integrated likelihood functions for non-Bayesian inference," Biometrika, Biometrika Trust, vol. 94(3), pages 529-542.
    5. 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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