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Communication Dans Un Congrès Année : 2014

Density and Distribution Function estimation through iterates of fractional Bernstein Operators

C. Manté

Résumé

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.
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Dates et versions

hal-01070827 , version 1 (02-10-2014)

Identifiants

  • HAL Id : hal-01070827 , version 1

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C. Manté. Density and Distribution Function estimation through iterates of fractional Bernstein Operators. 21st International Conference on Computational Statistics, Aug 2014, Genève, Switzerland. pp.335-342. ⟨hal-01070827⟩
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