|
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. Functional depths have been originally proposed for sample of curves that are measured on a dense and common grid. In practice, this is usually not the case, since curves are often observed at subject dependent and sparse grids. The main approach in the literature when dealing with sparse functional data consists on estimating the trajectories on a common and dense grid of points and using these estimated curves as observed data in the notion of depth. Our first goal in this study is to define a notion of depth that takes into account the estimation of the curves from sparse data and the uncertainty of the estimation. In the second part of this work we consider complex functional data, such as images, and we introduce depth-based location and dispersion measures. Permutation tests for comparing location and dispersion of two groups of images are proposed and calibrated. These statistical tools are applied to detect whether there are differences in the brain structure between healthy individuals and patients with specific mental disorders.
|
