Nonparametric regression on contaminated functional predictor with application to hyperspectral data
Résumé
Regressing nonparametrically a scalar response on a contaminated random curve observed at some measurement grid may be a hard task. To address this common statistical situation, a kernel presmoothing step is achieved on the noisy functional predictor. After that, the kernel estimator of the regression operator is built using the smoothed functional covariate instead of the original corrupted one. The rate of convergence is stated for this nested-kernel estimator with special attention to high-dimensional setting (i.e. the size of the measurement grid is much larger than the sample size). The proposed method is applied to simulated datasets in order to assess its finite-sample properties. Our methodology is further illustrated on a real hyperspectral dataset involving a supervised classification problem.