Articles | Volume 16, issue 22
Methods for assessment of models
16 Nov 2023
Methods for assessment of models |  | 16 Nov 2023

A diffusion-based kernel density estimator (diffKDE, version 1) with optimal bandwidth approximation for the analysis of data in geoscience and ecological research

Maria-Theresia Pelz, Markus Schartau, Christopher J. Somes, Vanessa Lampe, and Thomas Slawig

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Cited articles

Abramson, I. S.: On bandwidth variation in kernel estimates-a square root law, Ann. Stat., pp. 1217–1223,, 1982. a, b, c
Berlinet, A.: Hierarchies of higher order kernels, Prob. Theory Rel., 94, 489–504,, 1993. a
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Botev, Z. I., Grotowski, J. F., and Kroese, D. P.: Kernel density estimation via diffusion, Ann. Stat., 38, 2916–2957,, 2010. a, b, c, d, e, f, g, h, i, j, k, l, m, n
Short summary
Kernel density estimators (KDE) approximate the probability density of a data set without the assumption of an underlying distribution. We used the solution of the diffusion equation, and a new approximation of the optimal smoothing parameter build on two pilot estimation steps, to construct such a KDE best suited for typical characteristics of geoscientific data. The resulting KDE is insensitive to noise and well resolves multimodal data structures as well as boundary-close data.