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

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 def...

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Bibliographic Details
Published in:Statistics and computing 2011, Vol.21 (1), p.121-136
Main Authors: Dupuy, J.-F., Loubes, J.-M., Maza, E.
Format: Article
Language:English
Subjects:
Artificial Intelligence
Asymptotic properties
Computer Science
Consistency
Estimators
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Probability and Statistics in Computer Science
Statistical Theory and Methods
Statistics
Statistics and Computing/Statistics Programs
Stochasticity
Warpage
Warping
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Summary: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.
ISSN:0960-3174
1573-1375
DOI:10.1007/s11222-009-9152-9