Density kernel depth for outlier detection in functional data

Abstract

In this paper, we propose a novel approach to address the problem of functional outlier detection. Our method leverages a low-dimensional and stable representation of functions using Reproducing Kernel Hilbert Spaces (RKHS). We define a depth measure based on density kernels that satisfy desirable properties. We also address the challenges associated with estimating the density kernel depth. Throughout a Monte Carlo simulation we assess the performance of our functional depth measure in the outlier detection task under different scenarios. To illustrate the effectiveness of our method, we showcase the proposed method in action studying outliers in mortality rate curves.