A1141
Title: Block testing covariance and precision matrices for functional data analysis
Authors: Alessia Pini - Universita Cattolica del Sacro Cuore (Italy) [presenting]
Marie Morvan - Universite Rennes 1 (France)
Joyce Madison Giacofci - IRMAR - Universite Rennes (France)
Valerie Monber - Universite Rennes 1 (France)
Abstract: A method to test linear independence and conditional linear independence is proposed between portions of the domain of functional data. Data is assumed to be described by means of a B-splines basis expansion, such that coefficients of the basis expansion are directly related to the parts of the domain where the support of basis functions is strictly positive. The domain is further assumed to be partitioned into regions of interest. In such a case, the precision matrix is expected to have a block structure, where blocks correspond to elements of the partition. To infer which areas of the domain are conditionally independent of each other, a permutation test is proposed on blocks of the covariance or precision matrix of basis coefficients. A suitable strategy is introduced to deal with the multiple testing issues in this setting. It is shown that the procedure can identify the true structure of dependence on simulated data and on a real case study involving tractographic data related to the infrared emission spectra of fruit purees.
