%0 Journal Article
%T Application of iterated Bernstein operators to distribution function and density approximation
%+ Ecologie Marine et BIOdiversité (EMBIO)
%A Manté, Claude
%< avec comité de lecture
%Z MIO:12-017
%@ 0096-3003
%J Applied Mathematics and Computation
%I Elsevier
%V 218
%P 9156-9168
%8 2012
%D 2012
%R 10.1016/j.amc.2012.02.073
%K Non-parametric density estimator
%K Bernstein polynomials
%K Bona fide density
%K Optimal mesh
%K Hausdorff metric
%Z Statistics [stat]/Methodology [stat.ME]
%Z Statistics [stat]/Statistics Theory [stat.TH]
%Z Statistics [stat]/Applications [stat.AP]
%Z Sciences of the Universe [physics]/Continental interfaces, environment
%Z Mathematics [math]/Numerical Analysis [math.NA]
%Z Mathematics [math]/Statistics [math.ST]
%Z Environmental Sciences/Global ChangesJournal articles
%X 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.
%G English
%2 https://hal.science/hal-00740046/document
%2 https://hal.science/hal-00740046/file/BernDensAMCRevis.pdf
%L hal-00740046
%U https://hal.science/hal-00740046
%~ IRD
%~ SDE
%~ INSU
%~ UNIV-TLN
%~ CNRS
%~ UNIV-AMU
%~ MIO
%~ OSU-INSTITUT-PYTHEAS
%~ GIP-BE
%~ TDS-MACS
%~ MIO-EMBIO