  This article introduces a non parametric warping model for functional data.
When the outcome of an experiment is a sample of curves, data can be seen as
realizations of a stochastic process, which takes into account the small
variations between the different observed curves. The aim of this work is to
define a mean pattern which represents the main behaviour of the set of all the
realizations. So we define the structural expectation of the underlying
stochastic function. Then we provide empirical estimators of this structural
expectation and of each individual warping function. Consistency and asymptotic
normality for such estimators are proved.
