n-consistent density estimation in semiparametric regression models

The authors propose an estimator for the density of the response variable in the parametric mean regression model where the error density is left unspecified. With the application of empirical process theory, they derive its n-consistency and asymptotical normality. This result is further extended to models which allow possible parametric misspecification on the regression function and a special location-scale model. However, it is found that n-consistency breaks down in the presence of endogeneity. Monte Carlo simulations show that the proposed estimators have superior performance in finite sample compared to other density estimators available in the literature. Two real data illustrations reveal the advantage of the proposed density estimator over the Rosenblatt-Parzen kernel density estimator.