Conditional functional principal components analysis

Hervé Cardot (1)

1 LSP - Laboratoire de Statistique et Probabilités

This work proposes a non-parametric estimator of the regression function when the predictor is real and the dependent variable is a curve. The estimator is based on kernel smoothing. This approach is motivated by an extension of the functional principal components analysis, or Karhunen-Loève expansion, which can take into account non-parametrically the effects of an additional covariate. Such a model can also be interpreted as a non-parametric mixed effects model for functional data. Convergence rates are given for the regression function estimator and for the estimator of the conditional covariance operator. The good behaviour of the estimator for functional principal components analysis is illustrated on a simulation study.

Mots clés: covariance function; functional mixed effects; Karhunen Loève expansion; weighted covariance operator; eigenelements; almost sure convergence

Domaines: Statistiques [math.ST]

Hervé Cardot. Conditional functional principal components analysis. 2006. ⟨hal-00004472v2⟩