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Semiparametrically Efficient Estimation of Euclidean Parameters under Equality Constraints

Assume a (semi)parametrically efficient estimator is given of the Euclidean parameter in a (semi)parametric model. A submodel is obtained by constraining this model in that a continuously differentiable function of the Euclidean parameter vanishes. We present an explicit method to construct (semi)parametrically efficient estimators of the Euclidean parameter in such equality constrained submodels and prove their efficiency. Our construction is based solely on the original efficient estimator and the constraining function. Only the parametric case of this estimation problem and a nonparametric version of it have been considered in literature.