Functional outlier detection by a local depth with application to NOx levels

TL;DR

This paper introduces new outlier detection methods for functional data using kernelized functional spatial depth, demonstrating improved performance in simulations and real NOx emission data analysis.

Contribution

It develops three novel outlier detection procedures based on KFSD and provides a probabilistic thresholding approach for functional data.

Findings

Proposed methods outperform competitors in simulations

Effective detection of abnormal NOx emission curves

Thresholding approach accurately identifies outliers

Abstract

This paper proposes methods to detect outliers in functional data sets and the task of identifying atypical curves is carried out using the recently proposed kernelized functional spatial depth (KFSD). KFSD is a local depth that can be used to order the curves of a sample from the most to the least central, and since outliers are usually among the least central curves, we present a probabilistic result which allows to select a threshold value for KFSD such that curves with depth values lower than the threshold are detected as outliers. Based on this result, we propose three new outlier detection procedures. The results of a simulation study show that our proposals generally outperform a battery of competitors. We apply our procedures to a real data set consisting in daily curves of emission levels of nitrogen oxides (NOx) since it is of interest to identify abnormal NOx levels to take necessary environmental political actions.