Practical Uses of Kernel Density Estimators Perhaps this question is too broad, but I would like to know - how does one use a kernel density estimate in practice? I know of course that one can use it to draw pretty pictures on top of histograms, but what in particular can a KDE be used for that the empirical distribution itself cannot be used for, especially with the whole notion of needing to properly determine the correct bandwith?

Here's one place where KDE is more convenient than ECDF: inverse CDF technique for PRNG. Yes, you can in principle use ECDF too, but since ECDF is step function, its inverse is not continuous either, so you have to do some sort of interpolation between the observations. It's not as elegant as KDE.
