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Philippe Vieu, Paul Sabatier, Toulouse Print
Thursday, 24 April 2014, 12:15 - 13:15

Philippe Vieu, Université paul Sabatier, Toulouse

Semi-Parametric Modelling in Functional Data Analysis

Abstract: In usual multi- (but finite) -dimensional settings, semi-parametric ideas have been widely used in order to balance the trade-off betwen very few flexibility (this is the drawback of pure parametric modelling) and dimensional effects (this is the main drawback of non-parametric modelling).

In Functional Data Analysis (FDA)  one has to deal with continuous variables, that are variables being of infinite-dimensional nature (mainly curves but also images, arrays and other complex data). There has been a lot of attention these last years for developing parametric (mainly linear) models for FDA purpose, and even more recently non-parametric ideas have been developed in FDA. However, the infinite-dimensional nature of the problem makes the usual drawbacks described before even more important in FDA than in standard multivariate problems. From one side the high restrictivity of linear model is much more problematic for such highly complex data, while in the other hand the negative impact of the dimensionality on non-parametric methods is naturally very much higher in this infinite dimensional framework.

For these reasons, in a natural way, semi-parametric ideas have a great future in FDA. There are currently not so much advances in this field in the literature, and the aim of this talk will be to present some of them. It will be shown, mainly through the simple Single Functional Index Model, how semi-parametric modelling behaves for FDA. From a methodological point of view one will see how this model is rather flexible without being affected by the infinite-dimensionality effect. From an applied point of view, it will be highlighted how the functional semi-parametric statistical procedures are combining good predictive power and nice possibility of interpretation of the results.




Location: R42.2.113
Contact: Claude Adan, This e-mail address is being protected from spam bots, you need JavaScript enabled to view it