  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.
