  Averaging provides an alternative to bandwidth selection for density kernel
estimation. We propose a procedure to combine linearly several kernel
estimators of a density obtained from different, possibly data-driven,
bandwidths. The method relies on minimizing an easily tractable approximation
of the integrated square error of the combination. It provides, at a small
computational cost, a final solution that improves on the initial estimators in
most cases. The average estimator is proved to be asymptotically as efficient
as the best possible combination (the oracle), with an error term that
decreases faster than the minimax rate obtained with separated learning and
validation samples. The performances are tested numerically, with results that
compare favorably to other existing procedures in terms of mean integrated
square errors.
