On Estimating Non-Uniform Density Distributions Using N Nearest Neighbors

• Autorzy: Woźniak, P. R. , Kruszewski, A.
• Języki publikacji: EN

Abstrakty

EN

We consider density estimators based on the nearest neighbors method applied to discrete point distributions in spaces of arbitrary dimensionality. If the density is constant, the volume of a hypersphere centered at a random location is proportional to the expected number of points falling within the hypersphere radius. The distance to the N-th nearest neighbor alone is then a sufficient statistic for the density. In the non-uniform case the proportionality is distorted. We model this distortion by normalizing hypersphere volumes to the largest one and expressing the resulting distribution in terms of the Legendre polynomials. Using Monte Carlo simulations we show that this approach can be used to effectively address the trade-off between smoothing bias and estimator variance for sparsely sampled distributions.

Słowa kluczowe

EN

methods: statistical; methods: numerical

• Czasopismo: Acta Astronomica
• Rocznik: 2012
• Tom: Vol. 62, No. 4
• Strony: 409--417
• Opis fizyczny: Bibliogr. 9 poz., wykr.

Twórcy

autor

Woźniak, P. R.

• Los Alamos National Laboratory, Mail Stop B244, Los Alamos, NM 87545, USA ,

autor

Kruszewski, A.

• Warsaw University Observatory, Al. Ujazdowskie 4, 00-478 Warszawa, Poland ,

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