Abstract:
In recent years a variety of adjusted version of the profile likelihood and of the directed likelihood (or signed log likelihood ratio) have been proposed and studied. These versions are reviewed and compared, and some additional results are indicated.
Keywords:profile likelihood, directed likelihood, interest respecting reparametrizations, observed information, expected information matrix, information carrier, Cox–Reid “approximate conditional likelihood”, modified profile score, Lugannani–Rice approximation, stable and invariant adjustments.