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It is widely admitted that structured nonparametric modeling that circumventsthe curse of dimensionality is important in nonparametric estimation. In thispaper we show that the same holds for semi-parametric estimation. We argue thatestimation of the parametric component of a semi-parametric model can beimproved essentially when more structure is put into the nonparametric part ofthe model. We illustrate this for the partially linear model, and investigateefficiency gains when the nonparametric part of the model has an additivestructure. We present the semi-parametric Fisher information bound forestimating the parametric part of the partially linear additive model andprovide semi-parametric efficient estimators for which we use a smoothbackfitting technique to deal with the additive nonparametric part. We alsopresent the finite sample performances of the proposed estimators and analyzeBoston housing data as an illustration.

Semi-parametric regression: Efficiency gains from modeling the nonparametric part