= P-star approximation
{title2=$p^*(\widehat\theta\mid a;\theta)=c(\theta,a)|j(\widehat\theta)|^{1/2}e^{\ell(\theta)-\ell(\widehat\theta)}$}
= p\* approximation
{synonym}
For a regular model with a suitable <ancillary statistic> $a$, the displayed expression approximates the conditional density of the <maximum-likelihood estimator>. The normalizing factor includes $(2\pi)^{-p/2}$ for a $p$-dimensional estimator, depending on convention. The <observed information> is evaluated at the sample's own fitted value. In a pure scale model the factor is proportional to $1/\widehat\theta$; this <Jacobian determinant> can make the normalized approximation coincide with the exact conditional density.
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