An inferential approach for domain selection and profile monitoring of functional data
Alessia Pini

Inference for functional data is currently approached in two different ways: global inference aiming at testing functional hypotheses over the entire domain, and local inference aiming at selecting domain subsets responsible for the rejection of a null hypothesis.
In the local setting, a p-value can be computed at every point of the domain, obtaining an unadjusted p-value function, which controls only pointwise the probability of type I error: for all points, the probability of type I error is controlled, but the probability of committing at least one type I error (i.e., the the so-called familywise error rate - FWER) is not. The unadjusted p-value function cannot be used for domain selection purposes.
To deal with this problem, a non-parametric technique to adjust the p-value function is presented. The technique is provided with a control of the family wise error rate on domain intervals, and allows to perform domain selection. Several types of tests can be performed with this technique: for instance, functional t-test, tests on the parameters of functional ANOVA, function-on-scalar linear models. Finally, the technique can be used for supervised profile monitoring, improving the statistical performances of the monitoring techniques.