Consistency of semiparametric maximum likelihood estimators for two‐phase sampling

@article{Vaart2001ConsistencyOS,
  title={Consistency of semiparametric maximum likelihood estimators for two‐phase sampling},
  author={Aad van der Vaart and Jon A. Wellner},
  journal={Canadian Journal of Statistics},
  year={2001},
  volume={29}
}
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… 
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References

SHOWING 1-10 OF 35 REFERENCES
Large Sample Theory for Semiparametric Regression Models with Two-Phase, Outcome Dependent Sampling
Outcome-dependent, two-phase sampling designs can dramatically reduce the costs of observational studies by judicious selection of the most informative subjects for purposes of detailed covariate
Maximum Likelihood Estimation of Logistic Regression Parameters under Two‐phase, Outcome‐dependent Sampling
Outcome‐dependent sampling increases the efficiency of studies of rare outcomes, examples being case—control studies in epidemiology and choice–based sampling in econometrics. Two‐phase or double
Large sample theory of maximum likelihood estimates in semiparametric biased sampling models
Vardi [Ann. Statist. 13 178-203 (1985)] introduced an s-sample biased sampling model with known selection weight functions, gave a condition under which the common underlying probability distribution
E cient estimation for the proportional hazard model with interval censoring
The maximum likelihood estimator (MLE) for the proportional hazards model with case 1 interval censored data is studied. It is shown that the MLE for the regression parameter is asymptotically normal
Fitting regression models to case-control data by maximum likelihood
SUMMARY We consider fitting categorical regression models to data obtained by either stratified or nonstratified case-control, or response selective, sampling from a finite population with known
Semiparametric methods for response‐selective and missing data problems in regression
Suppose that data are generated according to the model f(y|x; θ) g(x), where y is a response and x are covariates. We derive and compare semiparametric likelihood and pseudolikelihood methods for
Existence and consistency of maximum likelihood in upgraded mixture models
Maximum Likelihood Estimation with Partially Censored Data
Suppose one observes independent samples of size n from both the mixture density ∫p(x|z)dη(z) and from the distribution η. The kernel p(x|z) is known. We show asymptotic normality and efficiency of
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