A gravitational approach to density estimation
M. Jiang and S.B. Provost (2008). A gravitational approach to density estimation. Journal of Statistical Research, Vol. 42, No. 2, pp. 181-194.
Abstract
It is shown that one can obtain a certain kernel density estimate at a given point
by assuming that the sample points and
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.
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