Université Paris 6Pierre et Marie Curie Université Paris 7Denis Diderot CNRS U.M.R. 7599 Probabilités et Modèles Aléatoires''

### Evolutionary Pareto distribution

Auteur(s):

Code(s) de Classification MSC:

• 62G07 Curve estimation (nonparametric regression, density estimation, etc.)
• 62G20 Asymptotic properties

Résumé: We consider here i.i.d. variables which are distributed according to a Pareto ${\cal P}(\alpha)$ up to some point $x_1$ and a Pareto ${\cal P}(\beta)$ (with a different parameter) after this point. We estimate the parameters by maximizing the likelihood of the sample, and investigate the rates of convergence and the asymptotic laws. We find here a problem which is very close to the change point question from the point of view of limiting of experiments. Especially, the rates of convergence and the limiting law of the estimators obtained here are identical as in a change point framework. Simulations are giving an illustration of the excellent quality of the procedure.

Mots Clés: change point ; Schauder basis ; likelihood process ; Pareto distribution

Date: 2001-05-07

Prépublication numéro: PMA-653