ON THE CONSISTENCY OF CONDITIONAL MAXIMUM LIKELIHOOD ESTIMATORS

J. PFANZAGL

Mathematical Institute, University of Cologne, Albertus-Magnus-Platz, D-50923 Cologne, Germany

(Received March 10, 1992; revised November 2, 1992)

Abstract. Let {P_{ϑ,η} : ϑ ∈ Θ, η ∈ H} be a family of probability measures admitting a sufficient statistic for the nuisance parameter η. The paper presents conditions for consistency of (asymptotic) conditional maximum likelihood estimators for ϑ. 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 estimatorsequence.

Key words and phrases: Estimation, consistency, nuisance parameters, logistic distribution.