We derive an identity 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.
"An identity for the nonparametric maximum likelihood estimator in missing data and biased sampling models." Bernoulli 1 (4) 335 - 341, December 1995. https://doi.org/10.3150/bj/1193758710