Structural Tests in Regression on Functional Variable

  • Laurent Delsol
  • Frédéric Ferraty
  • Philippe Vieu
Conference paper
Part of the Contributions to Statistics book series (CONTRIB.STAT.)

Abstract

This work focuses on recent advances on the way general structural testing procedures can be constructed in regression on functional variable. Our test statistic is constructed from an estimator adapted to the specific model to be checked and uses recent advances concerning kernel smoothing methods for functional data. A general theoretical result states the asymptotic normality of our test statistic under the null hypothesis and its divergence under local alternatives. This result opens interesting prospects about tests for no-effect, for linearity, or for reduction dimension of the covariate. Bootstrap methods are then proposed to compute the threshold value of our test. Finally, we present some applications to spectrometric datasets and discuss interesting prospects for the future.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Laurent Delsol
    • 1
  • Frédéric Ferraty
    • 2
  • Philippe Vieu
    • 2
  1. 1.Université d’OrléansOrléansFrance
  2. 2.Institut de Mathématiques de ToulouseToulouseFrance

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