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ON KERNEL DENSITY ESTIMATION WITHOUT BUMPS IN THE TAILS

An empirical approach to bandwidth choice is proposed for nonpara-metric estimation of the tails of a probability density. It is an \equal-information" method, in that it uses approximately equal amounts of sample information to estimate the density at all points. In one respect it is related to nearest neighbour methods, although it produces substantially smoother estimates, without the spikes associated with nearest neighbour analysis. In the tails it enjoys low relative error, as well as low absolute error, and as a result the tail estimates do not exhibit the familiar \bumpy" appearance which impedes both modal analysis and qualitative interpretation of curve estimates. Indeed, one of the applications of our technique is to bump-hunting methods, where it allows standard approaches to be improved.