  In one-dimensional density estimation on i.i.d. observations we suggest an
adaptive cross-validation technique for the selection of a kernel estimator.
This estimator is both asymptotic MISE-efficient with respect to the monotone
oracle, and sharp minimax-adaptive over the whole scale of Sobolev spaces with
smoothness index greater than 1/2. The proof of the central concentration
inequality avoids "chaining" and relies on an additive decomposition of the
empirical processes involved.
