Effect of uncertain ancillary parameters on maximum likelihood estimates in dynamic models

The behavior of maximum likelihood (ML) parameter estimates in dynamic models is considered here. In particular, we present results useful in examining the effect that imprecisely known ancillary-or nuisance-parameters have on ML estimates of the parameters of interest. The methodology relies on a certain derivative-based approximation which is obtained using the implicit function theorem. This approximation can be used to do deterministic sensitivity studies or to adjust confidence intervals. Several theoretical results are presented that relate quantities derived from this approximation to those that would be obtained from the corresponding exact expression.