OperaV1, Main, Exploration, bibRecord, 000286

Density and Distribution Function estimation through iterates of fractional Bernstein Operators

Identifieur interne : 000286 ( Main/Exploration ); précédent : 000285; suivant : 000287

Density and Distribution Function estimation through iterates of fractional Bernstein Operators

Auteurs : Claude Manté [France]

Source :

RBID : Hal:hal-01070827

English descriptors

mix :
- Bernstein operator, Bernstein polynomials, Density Estimation, Lagrange polynomials, root of operators.

Abstract

We describe a method for distribution function and density estimation with Bern- stein polynomials. We take advantage of results about the eigenstructure of the Bernstein operator to re ne the Sevy's convergence acceleration method, based on iterates of this opera- tor; the original Sevy's algorithm is improved by introducing fractional operators. The proposed algorithm has better convergence properties than the classical one; the price to pay is a control- lable loss of the shape-preserving properties of the Bernstein approximation (monotonicity and positivity in the Density Estimation setting). The method is tested on simulated data.

Url:

https://hal.archives-ouvertes.fr/hal-01070827

Affiliations:

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Le document en format XML

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<front><div type="abstract" xml:lang="en">We describe a method for distribution function and density estimation with Bern- stein polynomials. We take advantage of results about the eigenstructure of the Bernstein operator to re ne the Sevy's convergence acceleration method, based on iterates of this opera- tor; the original Sevy's algorithm is improved by introducing fractional operators. The proposed algorithm has better convergence properties than the classical one; the price to pay is a control- lable loss of the shape-preserving properties of the Bernstein approximation (monotonicity and positivity in the Density Estimation setting). The method is tested on simulated data.</div>
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Density and Distribution Function estimation through iterates of fractional Bernstein Operators

Density and Distribution Function estimation through iterates of fractional Bernstein Operators

Source :

English descriptors

Abstract

Links toward previous steps (curation, corpus...)

Le document en format XML

Pour manipuler ce document sous Unix (Dilib)

Pour mettre un lien sur cette page dans le réseau Wicri