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Linear predictive functional model on environmental data: modeling choices. (Modèle linéaire de prédiction fonctionnelle sur données environnementales: choix de modélisation.) (French. English summary) Zbl 1316.62002

Summary: Functional data analysis (FDA) has become in recent years an important field in statistics, because more data observed in different domains are in the shape of curves (meteorology, economics, linguistics,…). One tool in FDA is the fully functional linear model, which is used in the particular case where the variable to be predicted and the predictor are both curves. This model has been the subject of extensive theoretical research, but applications using it are few in number to date. We propose in this paper a methodological approach through an application of this model on light and chlorophyll a oceanographic profiles. It is used here to predict chlorophyll a profiles from derivatives of light data. The methodological approach helps to clarify modeling choices necessary to treat oceanographic profiles. Questions through our case study include the choice of the type and the number of basis functions to use, the choice of the value of the smoothing parameter and the goodness of fit criterion. We show that the utilisation of the functional linear model provides a good quality of reconstruction to access high frequency variations of chlorophyll a profiles at fine scale.

MSC:

62-07 Data analysis (statistics) (MSC2010)
62J05 Linear regression; mixed models
62P12 Applications of statistics to environmental and related topics
86A32 Geostatistics
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