  In the context of kernel density estimation, we give a characterization of
the kernels for which the parametric mean integrated squared error rate
$n^{-1}$ may be obtained, where $n$ is the sample size. Also, for the cases
where this rate is attainable, we give an asymptotic bandwidth choice that
makes the kernel estimator consistent in mean integrated squared error at that
rate and a numerical example showing the superior performance of the
superkernel estimator when the bandwidth is properly chosen.
