Estimating additive nonparametric models by partial L-q norm: The curse offractionality

We propose a new method for estimating additive nonparametric regression mo dels based on taking the L-q median of a sample of kernel estimators. We es tablish the consistency and asymptotic normality of our procedures. The rat e of convergence depends on the value of q. For q > (3)/(2) one has the,usu al one-dimensional rate, but if q the rate can be slower.