Adjusted Versions of Profile Likelihood and Directed Likelihood, and Extended Likelihood
讨论了轮廓似然和定向似然（即符号对数似然比）的几种调整版本，分为两组，分别与修正轮廓似然和修正定向似然密切相关；还提出了扩展似然的概念，将类似似然的函数与某些组合量关联起来。
SUMMARY Several adjusted and invariant versions of profile likelihood and of directed likelihood (short for signed log-likelihood ratio) are discussed. These adjusted versions, which fall into two groups, are closely related to modified profile likelihood and modified directed likelihood. The first group has the advantage of not requiring an explicit specification of an ancillary, but partly at a cost of a loss of asymptotic accuracy in comparison with the modified versions. The second group consists of some asymptotically sharpened versions of modified profile likelihood. Furthermore, a concept of extended likelihood is proposed, which associates a likelihood-like function to certain combinants. At the end, the relationship between adjusted profile likelihoods on the one hand and adjusted directed likelihoods on the other is discussed briefly, and in this context a close connection is established between modified profile likelihood and the extended likelihood determined by the modified directed likelihood.