Efficient Estimation of Additive Partially Linear Models

I consider the problem of estimating an additive partially linear model using general series estimation methods with polynomial and splines as two leading cases. I show that the finite‐dimensional parameter is identified under weak conditions. I establish the root‐n‐normality result for the finite‐dimensional parameter in the linear part of the model and show that it is asymptotically more efficient than a semiparametric estimator that ignores the additive structure. When the error is conditional homoskedastic, my finite‐dimensional parameter estimator reaches the semiparametric efficiency bound. Efficient estimation when the error is conditional heteroskedastic is also discussed.