MOX Report on Functional Boxplot Inflation Factor adjustment through Robust Covariance Estimators

A new MOX report entitled "Functional Boxplot Inflation Factor adjustment through Robust Covariance Estimators" by Rossi, A.; Cappozzo, A.; Ieva, F. has appeared in the MOX Report Collection. The report can be donwloaded at the following link: Abstract: The accurate identification of anomalous curves in functional data analysis (FDA) is of utmost importance to ensure reliable inference and unbiased estimation of parameters. However, detecting outliers within the infinite-dimensional space that encompasses such data can be challenging. In order to address this issue, we present a novel approach that involves adjusting the fence inflation factor in the functional boxplot, a widely utilized tool in FDA, through simulation-based methods. Our proposed adjustment method revolves around controlling the proportion of observations considered anomalous within outlier-free replications of the original data. To accomplish this, state-of-the-art robust estimators of location and scatter are employed. In our study, we compare the performance of multivariate procedures, which are suitable for addressing the challenges posed by the "small N, large P" problems, and functional operators for implementing the tun! ing proce ss. A simulation study and a real-data example showcase the validity of our proposal.