Error structures and parameter estimation

The error calculus based on the theory of Dirichlet forms is an extension of 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 one to lay the foundation of an infinite dimensional empirical error calculus. To cite this article: N. Bouleau, C. Chorro, C. R. Acad. Sci. Paris, Ser. I 338 (2004).