Title: On robust nonparametric techniques for dealing with the analysis of high dimensional data
Authors: Francesca Ieva - Politecnico di Milano (Italy) [presenting]
Anna Maria Paganoni - MOX-Politecnico di Milano (Italy)
Juan Romo - Universidad Carlos III de Madrid (Spain)
Nicholas Tarabelloni - Politecnico di Milano (Italy)
Abstract: The aim is to gather recently proposed statistical methods that deal with the robust inferential analysis of univariate and multivariate functional data. Functional Data Analysis (FDA) has seen an impressive growth in the statistical research due to the more and more frequent production of complex data in many different contexts (healthcare, environmental, engineering, etc.). According to the FDA model, data can be seen as measurements of a given quantity (or set of quantities) along an independent and continuous indexing variable (time or space). Observations are treated as random functions and can be viewed as trajectories of stochastic processes defined on a given infinite dimensional functional space. Even if the research in FDA dates back to 1970s, the major achievements have been reached in the last decade, especially in the multivariate setting. Despite the usefulness of robust statistics in this field, their generalization to the functional framework is definitely not straightforward, due to the infinite-dimensional nature of the spaces embedding data. A possibility is then to leverage on the concept of depth measures in order to create proper order statistics to be used in a suitable robust inferential framework. Topics like efficient methods for outlier detection and related graphical tools, as well as inferential tools for testing differences and dependency among families of curves will be discussed, presenting challenging applications.