Nonparametric estimation of an additive model with a link function

Joel L. Horowitz, Enno Mammen
2004 Annals of Statistics  
This paper describes an estimator of the additive components of a nonparametric additive model with a known link function. When the additive components are twice continuously differentiable, the estimator is asymptotically normally distributed with a rate of convergence in probability of n^-2/5. This is true regardless of the (finite) dimension of the explanatory variable. Thus, in contrast to the existing asymptotically normal estimator, the new estimator has no curse of dimensionality.
more » ... r, the estimator has an oracle property. The asymptotic distribution of each additive component is the same as it would be if the other components were known with certainty.
doi:10.1214/009053604000000814 fatcat:vzmbi5juovc75odefio7ks7eaq