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On confidence intervals associated with the usual and adjusted likelihoods
Author(s) -
Mukerjee R.,
Reid N.
Publication year - 1999
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/1467-9868.00212
Subject(s) - frequentist inference , confidence interval , statistics , mathematics , confidence distribution , nuisance parameter , credible interval , restricted maximum likelihood , coverage probability , likelihood principle , maximum likelihood , bayesian probability , likelihood function , bayesian inference , estimator , quasi maximum likelihood
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.