A maximum likelihood estimator for models containing nuisance parameters is proposed. The estimator is shown to be asymptotically normal and attain the semiparametric efficiency bounds for a number of important econometric models. The idea is to find a parametric model that passes through the true model. The score for the parametric model is then estimated nonparametrically and the estimator is obtained by setting the estimated score to zero.
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Chunrong Ai (1997) studied this question.
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