- Density and Distribution Function estimation through iterates of fractional Bernstein Operators hal link

Auteur(s): Mante C.

Conference: 21st International Conference on Computational Statistics (Genève, CH, 2014-08-19)
Actes de conférence: Proceedings of COMPSTAT 2014, vol. p.335-342 (2014)

Ref HAL: hal-01070827_v1
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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.