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

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