Plug-in semiparametric estimating equations

In parametric regression problems, estimation of the parameter of interest is typically achieved via the solution of a set of unbiased estimating equations. We are interested in problems where in addition to this parameter, the estimating equations consist of an unknown nuisance function which does not depend on the parameter. We study the effects of using a plug-in nonparametric estimator of the nuisance function (for example, a local-linear regression estimator) on the estimability of the parameter. In particular, we specify conditions on the functional estimator which ensure that the parametric rate of consistency for estimating the parameter of interest is preserved, and we give a general asymptotic covariance formula. We apply this theory to three examples.