On correcting for variance inflation in kernel density estimation

It is a simple matter to correct for the well-known variance inflation property of nonnegative kernel density estimates whereby the estimated distribution's variance exceeds that of the sample. But should we bother? Asymptotic mean integrated squared error considerations, developed here for the first time, suggest we may. However, we observe that the difference variance correction makes is, in most practical instances, negligible. Even when this is not so, exploratory conclusions would rarely be affected and, on occasions when this is not so either, variance correction can have a slight tendency to obscure potentially important features of the density. An exception to all this is estimation of the normal density for which correcting for variance inflation is certainty appropriate. This author retains a personal preference for continuing with uncorrected kernel density estimates, but the main message of the paper is the relative indifference to whether or not variance correction is employed. © 1991.