Asymptotic mean integrated squared errors of some nonparametric density estimators (Corresp.)

For estimation of a probability density function by an empirical function ,, based on a sample of size from , a widely used performance measure is the mean integrated squared error. For the wellknown -function type of , the asymptotic behavior of this measure is shown to be essentially unchanged if 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.