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On expected volumes of multidimensional confidence sets associated with the usual and adjusted likelihoods

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  • Gauri S. Datta
  • Thomas J. DiCiccio

Abstract

We consider a general multiparameter set‐up, where both the interest and the nuisance parameters are possibly vector valued. We derive an explicit higher order asymptotic formula to compare the expected volumes of confidence sets given by likelihood ratio statistics arising from the usual profile likelihood and various adjustments thereof. Our general framework also allows us to include highest posterior density regions, with approximate frequentist validity, in the study. The fact that our interest parameter is possibly vector valued complicates the derivation and warrants the development of special tools and techniques.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jorssb:v:63:y:2001:i:4:p:691-703
    DOI: 10.1111/1467-9868.00306
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    Cited by:

    1. Chang, In Hong & Mukerjee, Rahul, 2006. "Probability matching property of adjusted likelihoods," Statistics & Probability Letters, Elsevier, vol. 76(8), pages 838-842, April.
    2. 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.

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