Local inference on functional data based on the control of the family-wise error rate

In this work we focus on the problem of local inference for functional data. We describe a unified framework for testing hypotheses on functional data in a local perspective. The result of the testing procedures within the unified framework is an adjusted p-value function that can be used to select the areas of the domain responsible for the rejection of the null hypothesis. We discuss how different state of the art inferential procedures fall within the framework, and briefly describe a novel testing procedure with sound theoretical properties.