Title: Robust inverse regression for multivariate elliptical functional data Authors:  Eftychia Solea - Queen Mary University of London (United Kingdom) [presenting]
Abstract: Functional data have received significant attention as they frequently appear in modern applications, such as functional magnetic resonance imaging (fMRI). The infinite-dimensional nature of functional data makes it necessary to use dimension reduction techniques. Most existing techniques, however, rely on the covariance operator, which can be affected by heavy-tailed data and unusual observations. Therefore, we consider a robust functional sliced inverse regression (R-FSIR) for multivariate elliptical functional data. We define the elliptical distribution for a vector of random functions. We introduce a new statistical linear operator, called the conditional spatial sign Kendall's tau covariance operator, which can be seen as an extension of the multivariate Kendall's tau to both the conditional and functional settings, and is capable of handling heavy-tailed functional data and outliers. We show that the conditional spatial sign Kendall's tau covariance operator has the same eigenfunctions as the conditional covariance operator. Hence, we can formulate the generalized eigenvalue problem based on this new operator to achieve estimation robustness. We derive the convergence rates of the proposed estimators for both completely and partially observed data. Finally, we demonstrate the finite sample performance of our estimator using simulation examples and a real dataset based on fMRI.