  We address the problem of density estimation with $\mathbb{L}_s$-loss by
selection of kernel estimators. We develop a selection procedure and derive
corresponding $\mathbb{L}_s$-risk oracle inequalities. It is shown that the
proposed selection rule leads to the estimator being minimax adaptive over a
scale of the anisotropic Nikol'skii classes. The main technical tools used in
our derivations are uniform bounds on the $\mathbb{L}_s$-norms of empirical
processes developed recently by Goldenshluger and Lepski [Ann. Probab. (2011),
to appear].
