Risk upper bounds for RKHS ridge group sparse estimator in the regression model with non-Gaussian and non-bounded error

Abstract

We consider the problem of estimating a meta-model of an unknown regression model with non-Gaussian and non-bounded error. The meta-model belongs to a reproducing kernel Hilbert space constructed as a direct sum of Hilbert spaces leading to an additive decomposition including the variables and interactions between them. The estimator of this meta-model is calculated by minimizing an empirical least-squares criterion penalized by the sum of the Hilbert norm and the empirical $L^2$-norm. In this context, the upper bounds of the empirical $L^2$ risk and the $L^2$ risk of the estimator are established.