Robust inference in Fucntional Data Analysis

BOENTE, GRACIELA

Wollongong

Conferencia; International Conference on Robust Statistics (ICORS 2017); 2017

University of Wollongong, NIASRA, AMSI

Functional data analysis provides modern analytical tools for data that are recoded as images or as a continuous phenomenon over a period of time. Because of the intrinsic nature of these data, they can be viewed as realizations of random functions often assumed to be in a Hilbert space such as L2(I), with I a real interval or a finite dimensional Euclidean set. In particular, functional principal components or functional canonical correlation are statisticalprocedures developed to reduce the dimensionality retaining as much information as possible with respect to the measure of interest. To be more precise, the first q functional principal components provide the best q-dimensional approximation to random elements in Hilbert spaces, while functional canonical correlation is a tool to quantify correlations between pairs of observedrandom curves for which a sample is available. On the other hand, partial linear modelling ideas have recently been adapted to situations in which functional data are observed. More precisely, two generalizations have been considered todeal with the problem of predicting a real-valued response variable using explanatory variables that include a functional element, usually a random function, and a random variable. The semi-functional partial linear regression model allows the functional explanatory variables to act in a free nonparametric manner, while the scalar covariate corresponds to the linear component. Onthe other hand, the so{called functional partial linear model assumes that the scalar response is explained by a linear operator of a random function and a nonparametric function of a real-valued random variable.We will briefly discuss some approaches leading to obtain estimators of the principal directions in these situations less sensitive to atypical observations. In particular, the robust procedures developed to estimate the principal directions are used to develop robust methods under a functional partial linear model. If possible, we will also discuss methods to provide robust inferences for the canonical functions.