Abstract
Let {P ϑ, η : 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 estimator-sequence.
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Pfanzagl, J. On the consistency of conditional maximum likelihood estimators. Ann Inst Stat Math 45, 703–719 (1993). https://doi.org/10.1007/BF00774782
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DOI: https://doi.org/10.1007/BF00774782