Error structures and parameter estimation

Nicolas Bouleau (1) , Christophe Chorro (2)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique
2 CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique

This article proposes and studies 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. Here we show that this connection behaves well towards changes of variables and is related to the theory of asymptotic statistics. Finally the study of products permits to lay the premise of an infinite dimensional empirical error calculus.

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

Domaines: Probabilités [math.PR]

Nicolas Bouleau, Christophe Chorro. Error structures and parameter estimation. Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2004, 338, pp.305-310. ⟨hal-00287705⟩