Title: Estimating the response density in semiparametric regression
Authors: Ursula Mueller - Texas A and M University and University of Hamburg (Germany) [presenting]
Abstract: The focus is on regression models with a parametric (linear or nonlinear) regression function. We assume that the errors have mean zero and are independent of the covariates. The independence assumption enables us to construct a convolution type estimator for the response density that, in general, converges at a faster rate than the usual density estimators. If the regression function is invertible, the estimator converges with the optimal parametric root-$n$ rate. Otherwise the root-$n$ rate cannot be achieved. If the regression function is a step function, we can construct a response density estimator that has the same bias as the usual estimators based on the responses, but a smaller asymptotic variance.