K-narest neighbour kernel density estimation, the choice of optimal k

Abstract

The k-nearest neighbour kernel density estimation method is a special type of the
kernel density estimation method with local choice of the bandwidth. An advantage of
this estimator is that smoothing varies according to the number of observations in a
particular region. The crucial problem is how to estimate the value of the parameter
k. In the paper we discuss the problem of choosing the parameter k in a way that
minimizes the value of the asymptotic mean integrated square error (AMISE). We
dene the class of the modied cosine densities that meet the requirements given by
the AMISE. The results are compared in a simulation study.