Cox, D. R.; Reid, N. Parameter orthogonality and approximate conditional inference (with discussion). (English) Zbl 0616.62006 J. R. Stat. Soc., Ser. B 49, 1-39 (1987). This paper considers inference for a scalar parameter in the presence of one or more nuisance parameters which are required to be orthogonal to the parameter of interest. The construction and interpretation of orthogonalized parameters is discussed in some detail. A likelihood ratio statistic is proposed, which is constructed from the conditional distribution of the observations, given maximum likelihood estimates for the nuisance parameters. Reviewer: N.U.Prabhu Cited in 28 ReviewsCited in 348 Documents MSC: 62A01 Foundations and philosophical topics in statistics 62F99 Parametric inference 62F10 Point estimation Keywords:parameter orthogonality; approximate conditional inference; modified profile likelihood; normal transformation model; asymptotic theory; expected Fisher information matrix; nuisance parameters; likelihood ratio statistic; maximum likelihood estimates PDFBibTeX XMLCite \textit{D. R. Cox} and \textit{N. Reid}, J. R. Stat. Soc., Ser. B 49, 1--39 (1987; Zbl 0616.62006)