ON THE CONSISTENCY OF CONDITIONAL MAXIMUM-LIKELIHOOD ESTIMATORS

Let {P(upsilon),eta : upsilon is-an-element-of theta, eta is-an-element-of H} be a family of probability measures admitting a sufficient statistic for the nuisance parameter eta. The paper presents conditions for consistency of (asymptotic) conditional maximum likelihood estimators for upsilon. 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.