Non parametric estimation of the structural expectation of a stochastic increasing function

Jean-François Dupuy (1) , Jean-Michel Loubes (1) , Elie Maza (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

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.

Mots clés: Functional data analysis; Non parametric warping model; Structural expectation; Curve registration

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Jean-François Dupuy, Jean-Michel Loubes, Elie Maza. Non parametric estimation of the structural expectation of a stochastic increasing function. 2008. ⟨hal-00347829⟩