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Article Dans Une Revue Applied Mathematics and Computation Année : 2012

Application of iterated Bernstein operators to distribution function and density approximation

Résumé

We propose a density approximation method based on Bernstein polynomials, consisting in superseding the classical Bernstein operator by a convenient number I* of iterates of a closely related operator. We mainly tackle two difficulties met in processing real data, sampled on some mesh X-N. The first one consists in determining an optimal sub-mesh X-K*, in order that the operator associated with X-K* can be considered as an authentic Bernstein operator (necessarily associated with a uniform mesh). The second one consists in optimizing I in order that the approximated density is bona fide (positive and integrates to one). The proposed method is tested on two benchmarks in Density Estimation, and on a grain-size curve. (C) 2012 Elsevier Inc. All rights reserved.
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Dates et versions

hal-00740046 , version 1 (06-12-2013)

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Claude Manté. Application of iterated Bernstein operators to distribution function and density approximation. Applied Mathematics and Computation, 2012, 218, pp.9156-9168. ⟨10.1016/j.amc.2012.02.073⟩. ⟨hal-00740046⟩
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