|Density and Distribution Function estimation through iterates of fractional Bernstein Operators |
Auteur(s): Mante C.
Conference: 21st International Conference on Computational Statistics (Genève, CH, 2014-08-19)
Ref HAL: hal-01070827_v1
Exporter : BibTex | endNote
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.