A gravitational approach to density estimation

It is shown that one can obtain a certain kernel density estimate at a given
point x by assuming that the sample points and x are subject to the law of
universal gravitation or some variant thereof. Some distributional properties of
the resulting kernel are discussed, including the asymptotic normality of a certain
rescaled kernel. A two-stage algorithm for the selection of an optimal bandwidth
is described. The proposed density estimation technique is applied to three widely
used data sets.