  Consistency of the kernel density estimator requires that the kernel
bandwidth tends to zero as the sample size grows. In this paper we investigate
the question of whether consistency is possible when the bandwidth is fixed, if
we consider a more general class of weighted KDEs. To answer this question in
the affirmative, we introduce the fixed-bandwidth KDE (fbKDE), obtained by
solving a quadratic program, and prove that it consistently estimates any
continuous square-integrable density. We also establish rates of convergence
for the fbKDE with radial kernels and the box kernel under appropriate
smoothness assumptions. Furthermore, in an experimental study we demonstrate
that the fbKDE compares favorably to the standard KDE and the previously
proposed variable bandwidth KDE.
