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Title: Local inference for functional-on-scalar mixed models Authors:  Alessia Pini - Università Cattolica del Sacro Cuore (Italy) [presenting]
Helle Sorensen - University of Copenhagen (Denmark)
Anders Tolver - University of Copenhagen (Denmark)
Simone Vantini - Politecnico di Milano (Italy)
Abstract: The problem of performing nonparametric inference on the parameters of a functional-on-scalar mixed effect model is addressed. We perform inference in a local perspective, i.e., defining an adjusted p-value function for each parameter of the model. Such adjusted p-value functions can be thresholded at level alpha to select the regions of the domain presenting statistically significant effects. We show that the p-value functions are provided with an interval-wise control of the family wise error rate. In detail, the probability of wrongly selecting as significant a region of the domain where the null hypothesis is true is always controlled. Since inference is carried out by means of nonparametric permutation tests, the procedure will be exact regardless of the distribution of the functional data, and the sample size. We apply the proposed procedure to test differences between the 3D acceleration curves of trotting horses.