NPinR4FUN - Nonparametrics for Inference and Robustification for Functional Data

Anna Maria Paganoni-Nicholas Tarabelloni

MOX Dipartimento di Matematica, Politecnico di Milano

Friday 18th March 2016

14:30:00

ATTENZIONE: 3° piano Aula Seminari, Dipartimento di Matematica, Politecnico di Milano

The aim of the talk is to shed some lights on the recent developments of robust and non-parametric methods for the analysis of functional data. First of all, we will present the extension to functional data of depth measures and epigraphic indexes enabling the introduction of ranks and rank-based inference in such infinite-dimensional context. Statistical depths are non-parametric tools to measure the centrality of an observation with respect to a distribution of functions, and naturally bring along the notion of amplitude outlier. For this reason, they are used to build an extension of the boxplot to functional data and therefore to robustify a sample of observations. In opposition to amplitude outliers, a completely new kind of outlyingness arises as specific to functional data, that is the shape outlyingness. Recently, a powerful diagnostic tools, called outliergram and based on the use of Modified Band Depth (MBD) and Epigraphic Index (EI), has been proposed to identify shape outliers. Then, in the context of functional data, we will present correlation measures and independence tests based on generalisation of Kendall's tau and Spearman's rho coefficients, which have been recently proposed and are currently under study. Also, nonparametric extensions of quantiles to FDA have been advanced recently, and we will make use of this framework to solve the problem of calibrating a numerical model with functional response, aimed at reproducing a physiological ECG trace, to a functional dataset of real measurements. Many of these methods are implemented in an R package of recent development (roahd), which we will describe. contact: laura.sangalli@polimi.it