Multiple testing for outlier detection in functional data

Detecting outliers has become an increasing challenge in many areas, such as network intrusion detection, fraud detection, medical anomaly detection, and failure detection, as it was described by Chandola [1]. An outlier is basically a data that is significantly different from the normal behavior. In addition, several anomalies do not necessarily exhibit similar characteristics. Hence, detecting anomalies must be done by defining the normal behavior in the first place. Then, the deviation measured between an individual and the normal behavior gives good indications of anomalousness. However, as noticed in the same paper [1], defining a normal region that encompasses all the possible normal behaviors is sometimes really difficult. Moreover, an anomaly does not appear necessarily on all the explanatory variables, especially when the data is high-dimensional.