Kernel Depth Measures for Functional Data with Application to Outlier Detection

Abstract

In the last years the concept of data depth has been increasingly used in Statistics as a center-outward ordering of sample points in multivariate data sets. Data depth has been recently extended to functional data. In this paper we propose a new intrinsic functional data depth based on the representation of functional data on Reproducing Kernel Hilbert Spaces, and test its performance against a number of well known alternatives in the problem of functional outlier detection.