On the consistency of conditional maximum likelihood estimators

Let {P _, : , H} be a family of probability measures admitting a sufficient statistic for the nuisance parameter . The paper presents conditions for consistency of (asymptotic) conditional maximum likelihood estimators for . An application to the Rasch-model (a stochastic model for psychological tests) yields a condition on the sequence of nuisance parameters which is sufficient for strong consistency of conditional maximum likelihood estimators, and necessary for the existence of any weakly consistent estimator-sequence.