Suppose that a random sample of size n is drawn from a statistical model \({\mathcal M}\) of probability density p(x;\(\omega)\) where the parameter \(\omega\) is assumed to be uniquely expressed by \(\chi \in R^ d\) and \(\Psi \in R^ f\). Let \({\hat \omega}\) be the maximum likelihood estimator of \(\omega\) under \({\mathcal M}\) and let 1(\(\omega)\) be the log likelihood. Further let \({\mathcal M}_{\Psi}\) be a submodel obtained by fixing \(\Psi\) in \({\mathcal M}\). Suppose that (\({\hat \omega}\),a\({}_ 0)\) is minimal sufficient under \({\mathcal M}\) such that \(a_ 0\) is approximately ancillary and the conditional density of \({\hat \omega}\) for given \(a_ 0\) satisfies \[ p({\hat \omega};\omega | a_ 0)=[const.| j({\hat \omega})|^{1/2}\exp \{l(\omega)-l({\hat \omega})\}][1+O(n^{- 3/2})] \] where \(j(\omega)=\partial^ 2l(\omega)/\partial \omega \partial \omega^ t\). Then it is shown in this paper that there exists a statistic \(r^*_{\Psi}\) of dimension f under \({\mathcal M}_{\Psi}\) which follows f-dimensional normal distribution N(0,I) to relative order \(O(n^{-3/2})\). This is used to get confidence regions for the partial parameter \(\Psi\), independently of the nuisance parameter \(\chi\). When \(f=1\), \(r^*_{\Psi}\) is obtained by adjusting the mean and variance of the signed log likelihood ratio statistic given by \[ \{sgn({\hat \Psi}- \Psi)\}[2\{l({\hat \omega})-l({\hat \chi}_{\Psi},\Psi)\}]^{1/2}, \] where \({\hat \chi}_{\Psi}\) stands for the maximum likelihood estimator of \(\chi\) under the model \({\mathcal M}_{\Psi}\).