Efficient estimation in conditional single-index regression

Semiparametric single-index regression involves an unknown finite-dimensional parameter and an unknown (link) function. We consider estimation of the parameter via the pseudo-maximum likelihood method. For this purpose we estimate the conditional density of the response given a candidate index and maximize the obtained likelihood. We show that this technique of adaptation yields an asymptotically efficient estimator: it has minimal variance among all estimators.Single-index model Pseudo-maximum likelihood Semiparametric efficiency bound