Extracting informative features in functional datasets: statistical methods with applications in spectrometry

• Philippe Vieu ^[1]
  1. [1] Institut de Mathmatiques, Toulouse, France
• Localización: XII Congreso Galego de Estatística e Investigación de Operacións: Lugo, 22-23-24 de outubro de 2015. Actas / María José Ginzo Villamayor (ed. lit.), José María Alonso Meijide (ed. lit.) , Luis Alberto Ramil Novo (ed. lit.), 2015, ISBN 978-84-8192-522-7, págs. 4-4
• Idioma: inglés
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• Resumen

  • In this talk we will look at regression problem with continuous covariates χ and scalar response Y . The main goal of the talk is to emphasize on exploratory questions through the search of what are the specific features in the functional covariate χ which are acting on the response Y . When the covariate is a function χ = χ(t), t ∈ [a, b] this question may take various forms, like: • Which derivative(s) of χ is(are) the most informative for explaining Y ? • Is there some subinterval [c, d] ⊂ [a, b] containing all informations for predicting Y ? • Can the curve χ be summarized by a small number of discretized values? The presentation will be mainly methodological with the presentation of various approaches which have been developed in the last few years in Functional Data Analysis. The methodologies will be illustrated by means of various real datasets coming from spectrometrics in which χ will be the absorbance channel of some element (meat, orange juice, sugar, . . .) as function of the spectrum wavelengths and in which Y will be some chemical componant of the element (fatness, moisture, . . .) to be predicted from the spectrum. Asymptotics issues/results will only be briefly mentionned. The methods to be presented will be linked with various topics of Statistics being of great current actuality (nonparametric statistics, semiparametric statistics, goodness of fit test, variable selection, . . .). The main general point that will be supported in this talk is the fact that most of the modern statistical techniques (previously introduced for finite dimensional problems) may have (pending to suitable functional adaptations . . .) great interest in Functional Data Analysis.