No effect tests in regression on functional variable and some applications to spectrometric studies

Recent advances in structural tests for regression on functional variable are used to construct test of no effect. Various bootstrap procedures are considered and compared in a simulation study. These tests are finally applied on real world datasets dealing with spectrometric studies using the information collected during this simulation study. The results obtained for the Tecator dataset are relevant and corroborated by former studies. The study of a smaller dataset concerning corn samples shows the efficiency of our method on small size samples. Getting information on which derivatives (or which parts) of the spectrometric curves have a significant effect allows to get a better understanding of the way spectrometric curves influence the quantity to predict. In addition, a better knowledge of the structure of the underlying regression model may be useful to construct a relevant predictor. Copyright Springer-Verlag Berlin Heidelberg 2013