Université Paris 6
Pierre et Marie Curie | Université Paris 7
Denis Diderot | |

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**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*