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On confidence intervals associated with the usual and adjusted likelihoods

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  • R. Mukerjee
  • N. Reid

Abstract

In the presence of nuisance parameters, we drive an explicit higher order asymptotic formula to compare the expected lengths of confidence intervals given by likelihood ratio statistics arising from the usual profile likelihood and various adjustments thereof. Highest posterior density regions, with approximate frequentist validity, are also included in the study.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jorssb:v:61:y:1999:i:4:p:945-953
    DOI: 10.1111/1467-9868.00212
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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. Rahul Mukerjee & Ling-Yau Chan, 2009. "Confidence intervals based on empirical statistics: existence of a probability matching prior and connection with frequentist Bartlett adjustability," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(2), pages 271-282, August.
    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. Malay Ghosh & Gauri Datta & Dalho Kim & Trevor Sweeting, 2006. "Likelihood-based Inference for the Ratios of Regression Coefficients in Linear Models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(3), pages 457-473, September.
    5. In Chang & Rahul Mukerjee, 2006. "Asymptotic Results on a General Class of Empirical Statistics: Power and Confidence Interval Properties," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(3), pages 427-440, September.

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