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Functional Data Analysis for the Detection of Outliers and Study of the Effects of the COVID-19 Pandemic on Air Quality: A Case Study in Gijón, Spain

Author

Listed:
  • Xurxo Rigueira

    (CINTECX, GESSMin Group, Department of Natural Resources and Environmental Engineering, University of Vigo, 36310 Vigo, Spain)

  • María Araújo

    (CINTECX, GESSMin Group, Department of Natural Resources and Environmental Engineering, University of Vigo, 36310 Vigo, Spain)

  • Javier Martínez

    (CINTECX, GESSMin Group, Department of Applied Mathematics I, University of Vigo, 36310 Vigo, Spain)

  • Paulino José García-Nieto

    (Department of Mathematics, University of Oviedo, 33007 Oviedo, Spain)

  • Iago Ocarranza

    (Possible Incorporated SL, 36211 Vigo, Spain)

Abstract

Air pollution, especially at the ground level, poses a high risk for human health as it can have serious negative effects on the population of certain areas. The high variability of this type of data, which are affected by weather conditions and human activities, makes it difficult for conventional methods to precisely detect anomalous values or outliers. In this paper, classical analysis, statistical process control, and functional data analysis are compared for this purpose. The results obtained motivate the development of a new outlier detector based on the concept of functional directional outlyingness. The validation of this algorithm is perfomed on real air quality data from the city of Gijón, Spain, aiming to detect the proven reduction in NO 2 levels during the COVID-19 lockdown in that city. Three more variables ( SO 2 , PM 10 , and O 3 ) are studied with this technique. The results demonstrate that functional data analysis outperforms the two other methods, and the proposed outlier detector is well suited for the accurate detection of outliers in data with high variability.

Suggested Citation

  • Xurxo Rigueira & María Araújo & Javier Martínez & Paulino José García-Nieto & Iago Ocarranza, 2022. "Functional Data Analysis for the Detection of Outliers and Study of the Effects of the COVID-19 Pandemic on Air Quality: A Case Study in Gijón, Spain," Mathematics, MDPI, vol. 10(14), pages 1-27, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:14:p:2374-:d:856959
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    References listed on IDEAS

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    1. Gerda Claeskens & Mia Hubert & Leen Slaets & Kaveh Vakili, 2014. "Multivariate Functional Halfspace Depth," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 411-423, March.
    2. López-Pintado, Sara & Romo, Juan, 2009. "On the Concept of Depth for Functional Data," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 718-734.
    3. Chen, Yan-Kwang, 2004. "Economic design of control charts for non-normal data using variable sampling policy," International Journal of Production Economics, Elsevier, vol. 92(1), pages 61-74, November.
    4. Freeman, Jade & Modarres, Reza, 2006. "Inverse Box-Cox: The power-normal distribution," Statistics & Probability Letters, Elsevier, vol. 76(8), pages 764-772, April.
    5. Ricardo Fraiman & Graciela Muniz, 2001. "Trimmed means for functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(2), pages 419-440, December.
    6. Dai, Wenlin & Genton, Marc G., 2019. "Directional outlyingness for multivariate functional data," Computational Statistics & Data Analysis, Elsevier, vol. 131(C), pages 50-65.
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