A nonlinear aggregation type classifier

Supervised classification is still one of the hot topics for high dimensional and functional data due to the importance of their applications and the intrinsic difficulty in a general setup. In this context, there is a vast literature on classification methods which include: linear classification,k -nearest neighbors and kernel rules, classification based on partial least squares, reproducing kernels or depth measures. Complete surveys of the literature are the works by Ba ıllo et al. [1], Cuevas [13] and Delaigle and Hall [16]. In the book Contributions in infinite-dimensional statistics and related topics [7], there are also several recent advances in supervised and unsupervised classification. See for instance, Chapters 2, 5, 22 or 48, or directly, Chapter 1 of this issue (Bongiorno et al. [6]). In this context, very recently there have been of great interest to develop aggregation methods. In particular, there is a large list of linear aggregation methods like boosting (Breiman [8], Breiman [9]), random forest (Breiman [10], Biau et al. [3], Biau [5]), among others. All these methods exhibit an important improvement when combining a subset of classifiers to produce a new one. Most of the contributions to the aggregation literature have been proposed for nonparametric regression, a problem closely related to classification rules, which can be obtained just by plugging in the estimate of the regression function into the Bayes rule (see for instance, Yang [19] and Bunea et al. [11]).