Functional Outlier Detection and Taxonomy by Sequential Transformations

Abstract: Functional data analysis can be seriously impaired by abnormal observations, which can be classified as either magnitude or shape outliers based on their way of deviating from the bulk of data. Identifying magnitude outliers is relatively easy, while detecting shape outliers is much more challenging. We propose turning the shape outliers into magnitude outliers through data transformation and detecting them using the functional boxplot. Besides easing the detection procedure, applying several transformations sequentially provides a reasonable taxonomy for the flagged outliers. A joint functional ranking, which consists of several transformations, is also defined here. Simulation studies are carried out to evaluate the performance of the proposed method using different functional depth notions. Interesting results are obtained in several practical applications.