  In this article, we derive concentration inequalities for the
cross-validation estimate of the generalization error for stable predictors in
the context of risk assessment. The notion of stability has been first
introduced by \cite{DEWA79} and extended by \cite{KEA95}, \cite{BE01} and
\cite{KUNIY02} to characterize class of predictors with infinite VC dimension.
In particular, this covers $k$-nearest neighbors rules, bayesian algorithm
(\cite{KEA95}), boosting,... General loss functions and class of predictors are
considered. We use the formalism introduced by \cite{DUD03} to cover a large
variety of cross-validation procedures including leave-one-out
cross-validation, $k$-fold cross-validation, hold-out cross-validation (or
split sample), and the leave-$\upsilon$-out cross-validation.
  In particular, we give a simple rule on how to choose the cross-validation,
depending on the stability of the class of predictors. In the special case of
uniform stability, an interesting consequence is that the number of elements in
the test set is not required to grow to infinity for the consistency of the
cross-validation procedure. In this special case, the particular interest of
leave-one-out cross-validation is emphasized.
