arXiv subjects

Alba M. Franco-Pereira

Publications and source records attributed to Alba M. Franco-Pereira.

4 recordsLinked to original sources

arXiv2025

Area-based epigraph and hypograph indices for functional outlier detection

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.

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arXiv2025

Health Prognostics in Multi-sensor Systems Based on Multivariate Functional Data Analysis

Recent developments in big data analysis, machine learning, Industry 4.0, and IoT applications have enabled the monitoring and processing of multi-sensor data collected from systems, allowing for the prediction of the "Remaining Useful Life" (RUL) of system components. Particularly in the aviation industry, Prognostic Health Management (PHM) has become one of the most important practices for ensuring reliability and safety. Not only is the accuracy of RUL prediction important, but the implementability of techniques, domain adaptability, and interpretability of system degradation behaviors have also become essential. In this paper, the data collected from the multi-sensor environment of complex systems are processed using a Functional Data Analysis (FDA) approach to predict when the systems will fail and to understand and interpret the systems' life cycles. The approach is applied to the C-MAPSS datasets shared by National Aeronautics and Space Administration, and the behaviors of the sensors in aircraft engine failures are adaptively modeled with Multivariate Functional Principal Component Analysis (MFPCA). While the results indicate that the proposed method predicts the RUL competitively compared to other methods in the literature, it also demonstrates how multivariate Functional Data Analysis is useful for interpretability in prognostic studies within multi-sensor environments.

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arXiv2024

New stochastic comparisons based on tail values at risk

In this paper we provide a new criterion for the comparison of claims, when we have conditional claims arising in stop loss contracts or contracts with franchise deductible. These stochastic comparisons are made on the basis of the Tail Value at Risk (also known as conditional tail expectation), just for a fixed level and beyond. In particular, we explain the interest of comparing these quantities, study some preservation properties and, in addition, we provide sufficient conditions for its study. Finally we illustrate its usefulness with some examples.

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arXiv2024

Clustering multivariate functional data using the epigraph and hypograph indices: a case study on Madrid air quality

With the rapid growth of data generation, advancements in functional data analysis (FDA) have become essential, especially for approaches that handle multiple variables at the same time. This paper introduces a novel formulation of the epigraph and hypograph indices, along with their generalized expressions, specifically designed for multivariate functional data (MFD). These new definitions account for interrelationships between variables, enabling effective clustering of MFD based on the original data curves and their first two derivatives. The methodology developed here has been tested on simulated datasets, demonstrating strong performance compared to state-of-the-art methods. Its practical utility is further illustrated with two environmental datasets: the Canadian weather dataset and a 2023 air quality study in Madrid. These applications highlight the potential of the method as a great tool for analyzing complex environmental data, offering valuable insights for researchers and policymakers in climate and environmental research.

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