Estimating additive nonparametric models by partial Lq norm: the curse of fractionality

We propose a new method for estimating additive nonparametric regression models based on taking the Lq median of a sample of kernel estimators. We establish the consistency and asymptotic normality of our procedures. The rate of convergence depends on the value of q. For q > 3/2 one has the usual one-dimensional rate, but if q [less-than-or-equal] 3/2 the rate can be slower.