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An identity for the nonparametric maximum likelihood estimator in missing data and biased sampling models. (English) Zbl 0837.62030

Summary: We derive an indentity for the maximum likelihood estimator in nonparametric missing data models and biased sampling models, which almost says that this estimator is efficient. Application of empirical process theory to the identity provides us with a straightforward consistency and efficiency proof. The identity is illustrated with the random truncation model.

MSC:

62G05 Nonparametric estimation
62G30 Order statistics; empirical distribution functions
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