B0360
Title: A story of a functional depth through finite projections: An FPCA approach
Authors: Sara Armaut - LJAD - Universite de Nice (France) [presenting]
Thomas Laloe - LJAD - Universite de Nice (France)
Roland Diel - LJAD - Universite de Nice (France)
Abstract: Initially, the field of statistical depth for functional data is considered. Based on functional principal component analysis (FPCA), a new definition of a specific functional depth is provided called principal component functional depth (PCD). In this definition, projections are used which reduces to employing a given multivariate depth. These finite projections are somehow obtained by representing the data in terms of the eigenfunctions of the covariance operator and the associated functional principal components (FPCs) as usually done in FPCA. More precisely, the key ingredient in the approach is the well-known Karhunen-Love (KL) decomposition. In this method, a square-integrable zero-mean stochastic process can be represented as an infinite linear combination of orthogonal functions. The importance of the KL statement is that it generates the best orthogonal L2-basis in the sense that it minimizes the total mean squared error. One further interesting point in using the KL transform is that the infinite expansion may be truncated in a finite one in such a way that it may explain a high percentage of the variance. A basic analysis of depth properties and uniform consistency results for PCD is performed.
