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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 $ 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.

 

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