Semiparametrically Efficient Estimation of Euclidean Parameters under Equality Constraints

TL;DR

This paper introduces a method to construct efficient estimators for Euclidean parameters under equality constraints in both parametric and nonparametric models, building on existing efficient estimators.

Contribution

It provides an explicit, general approach to achieve semiparametric efficiency in constrained submodels using only the original estimator and the constraint function.

Findings

Explicit construction of efficient estimators under constraints

Proves efficiency of the proposed estimators

Applicable to both parametric and nonparametric models

Abstract

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.