Error structures and parameter estimation

Nicolas Bouleau (1) , Christophe Chorro (1, 2)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique
2 CES - Centre d'économie de la Sorbonne

This article proposes a link between statistics and the theory of Dirichlet forms used to compute errors. The error calculus based on Dirichlet forms is an extension of classical Gauss' approach to error propagation. The aim of this paper is to derive error structures from measurements. The links with Fisher's information lay the foundations of a strong connection with experiment. We show that this connection behaves well towards changes of variables and is related to the theory of asymptotic statistics.

Mots clés: Error; sensitivity; Dirichlet forms; squared field operator; Cramer-Rao inequality; Fisher information

Domaines: Probabilités [math.PR]; Théorie [stat.TH]; Statistiques [math.ST]; Analyse fonctionnelle [math.FA]

Nicolas Bouleau, Christophe Chorro. Error structures and parameter estimation. 2006. ⟨hal-00119494⟩