The famous p* formula provides a higher-order approximation for the conditional distribution of the maximum likelihood estimator given an exact ancillary. By collating well known existing results including application of a formal higher-order expansion the formula is generalized for the case of approximate ancillaries. Applied to the class of autoregressive models a case for conditional inference is made and the accuracy of the resulting approximation is demonstrated numerically.
Marsh, P. (in press). Approximation for the conditional distribution of the MLE with application to autoregression. Advances and applications in statistics, 42(1),