Title: Depth analysis for sparse functional data
Authors: Sara Lopez Pintado - Northeastern University (United States) [presenting]
Abstract: Functional data analysis is an exciting developing area in statistics where the basic unit of observation is a function. Many different statistical methods, such as principal components and regression, have been extended to functional data. In the last decade there has been an intensive development of different notions of data depth for functional data which have been proven to be a powerful robust nonparametric tool for analyzing functions. In general, a data depth is a function that measures the centrality of an observation within a population or sample. It provides a rigorous way of ranking observations from center-outward and of defining robust statistics such as medians and trimmed means. The notions of depth for functional data introduced in the literature are designed for sample of curves that are measured on a common and dense grid. In practice, curves are often observed at subject-dependent and sparse grids and therefore, they have to be first estimated in a common grid. Standard functional depth analysis has ignored the inherent uncertainty associated with the preliminary curve estimation step. We design a general procedure that allows the analysis of depth to explicitly address sparsity and to take curve uncertainty estimation into account. In a simulation study we show the performance of the proposed approach in different settings changing the types of sparsity of the simulated curves.