A0911
Title: Robust inverse regression for multivariate elliptical functional data
Authors: Eliana Christou - University of North Carolina at Charlotte (United States)
Jun Song - Korea University (Korea, South)
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) and natural language processing. 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. Thus, a robust sliced inverse regression is considered for multivariate elliptical functional data. Therefore, a new statistical linear operator is introduced, 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. The new operator is robust to heavy-tailed data and outliers and can provide a robust estimate of sufficient predictors. The convergence rates of the proposed estimators are also derived for both completely and partially observed data. Finally, the finite sample performance of the estimator is demonstrated using simulation examples and a real dataset based on fMRI.
