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Title: Depth-based methods for sparse and complex functional data Authors:  Sara Lopez Pintado - Northeastern University (United States) [presenting]
Abstract: Data depth is a well-known and useful notion in functional data analysis. It provides a center-outward ranking for a sample of curves. This ordering allows the definition of descriptive statistics such as medians, trimmed means and central regions for functional data. Moreover, data depth is often used as a building block for developing outlier-detection techniques and for robustifying standard statistical methods. We consider complex functional data such as images and we introduce depth-based location and dispersion measures. Permutation test for comparing location and dispersion of two groups of images are proposed and calibrated. In addition, techniques for detecting image outliers are introduced. The performances of these methods are illustrated in simulated and real data sets. We have also extended the notion of depth to sparse functional data where the functions are observed in subject dependent and/or sparse grids. In this case the functional data is an estimate of the underlying true curves and there is uncertainty in its estimation. We propose a notion of depth that takes into account this uncertainty.