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

  • Authors:

  • J. -F. Dupuy;J. -M. Loubes;E. Maza

  • Affiliations:

  • Laboratoire Mathématiques, Image et Applications, Université de La Rochelle, La Rochelle, France 17000;Université Toulouse 3, Institut de Mathématiques (UMR 5219), Toulouse, France 31062;Laboratoire Génomique et Biotechnologie des Fruits, INP-ENSAT (UMR 990), Castanet-Tolosan, France 31326

  • Venue:
  • Statistics and Computing
  • Year:
  • 2011

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Abstract

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 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.