Consistency of semiparametric maximum likelihood estimators for two-phase sampling. (English) Zbl 0976.62017

Summary: Semiparametric maximum likelihood estimators have recently been proposed for a class of two-phase, outcome-dependent sampling models. All of them were “restricted” maximum likelihood estimators, in the sense that the maximization is carried out only over distributions concentrated on the observed values of the covariate vectors.
In this paper, the authors give conditions for consistency of these restricted maximum likelihood estimators. They also consider the corresponding unrestricted maximization problems, in which the “absolute” maximum likelihood estimators may then have support on additional points in the covariate space. Their main consistency result also covers these unrestricted maximum likelihood estimators, when they exist for all sample sizes.


62F10 Point estimation
62F12 Asymptotic properties of parametric estimators
62G05 Nonparametric estimation
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