Under appropriate assumptions, expressions describing the asymptotic behavior of the bias and variance of k-nearest neighbor density estimates with weight function w are obtained. The behavior of these estimates is compared with that of kernel estimates. Particular attention is paid to the...

We consider the problem of estimating the shape parameters in the multi- variate Liouville model in the presence of an unknown infinite-dimensional parameter. We propose an ad hoc estimate and show that it is asymptotically efficient.