For estimation of a probability density functionfby an empirical functionf_{n},, based on a sample of sizenfromf, a widely used performance measure is the mean integrated squared error. For the wellknown\delta-function type off_{n}, the asymptotic behavior of this measure is shown to be essentially unchanged iff_{n}is replaced by a recursive version. Also, this asymptotic behavior is characterized under somewhat milder smoothness restrictions but stronger tail restrictions than previously considered in the literature.