Area-based epigraph and hypograph indices for functional outlier detection

TL;DR

This paper introduces new area-based indices for functional outlier detection that effectively identify both magnitude and shape anomalies, improving robustness over existing methods.

Contribution

The paper proposes ABEI and ABHI indices and a novel EHyOut procedure that recasts outlier detection as a multivariate problem, enhancing detection accuracy.

Findings

EHyOut outperforms benchmark methods in simulations.

Indices are stable across various contamination levels.

Method effectively detects both magnitude and shape outliers.

Abstract

Detecting outliers in Functional Data Analysis is challenging because curves can stray from the majority in many different ways. The Modified Epigraph Index (MEI) and Modified Hypograph Index (MHI) rank functions by the fraction of the domain on which one curve lies above or below another. While effective for spotting shape anomalies, their construction limits their ability to flag magnitude outliers. This paper introduces two new metrics, the Area-Based Epigraph Index (ABEI) and Area-Based Hypograph Index (ABHI) that quantify the area between curves, enabling simultaneous sensitivity to both magnitude and shape deviations. Building on these indices, we present EHyOut, a robust procedure that recasts functional outlier detection as a multivariate problem: for every curve, and for its first and second derivatives, we compute ABEI and ABHI and then apply multivariate outlier-detection techniques to the resulting feature vectors. Extensive simulations show that EHyOut remains stable across a wide range of contamination settings and often outperforms established benchmark methods. Moreover, applications to Spanish weather data and United Nations world population data further illustrate the practical utility and meaningfulness of this methodology.