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Modeling Air Pollution Using Partially Varying Coefficient Models with Heavy Tails

Author

Listed:
  • Nicole Jeldes

    (Department of Statistics, Universidad de Valparaíso, Valparaíso 2340000, Chile)

  • Germán Ibacache-Pulgar

    (Department of Statistics, Universidad de Valparaíso, Valparaíso 2340000, Chile
    Interdisciplinary Center for Atmospheric and Astro-Statistical Studies, Universidad de Valparaíso, Valparaíso 2340000, Chile)

  • Carolina Marchant

    (Faculty of Basic Sciences, Universidad Católica del Maule, Talca 3480112, Chile
    ANID-Millennium Science Initiative Program-Millennium Nucleus Center for the Discovery of Structures in Complex Data, Santiago 7820244, Chile)

  • Javier Linkolk López-Gonzales

    (Facultad de Ingeniería y Arquitectura, Universidad Peruana Unión, Lima 15464, Peru)

Abstract

The increase in air pollution levels in recent decades around the world has caused a negative impact on human health. A recent investigation by the World Health Organization indicates that nine out of ten people on the planet breathe air containing high levels of pollutants and seven million people die each year from this cause. This problem is present in several cities in South America due to dangerous levels of particulate matter present in the air, particularly in the winter period, making it a public health problem. Santiago in Chile and Lima in Peru are among the ten cities with the highest levels of air pollution in South America. The location, climate, and anthropogenic conditions of these cities generate critical episodes of air pollution, especially in the coldest months. In this context, we developed a semiparametric model to predict particulate matter levels as a function of meteorological variables. For this, we discuss estimation and diagnostic procedures using a Student’s t -based partially varying coefficient model. Parameter estimation is performed through the penalized maximum likelihood method using smoothing splines. To obtain the parameter estimates, we present a weighted back-fitting algorithm implemented in R-project and Matlab software. In addition, we developed local influence techniques that allowed us to evaluate the potential influence of certain observations in the model using four different perturbation schemes. Finally, we applied the developed model to real data on air pollution and meteorological variables in Santiago and Lima.

Suggested Citation

  • Nicole Jeldes & Germán Ibacache-Pulgar & Carolina Marchant & Javier Linkolk López-Gonzales, 2022. "Modeling Air Pollution Using Partially Varying Coefficient Models with Heavy Tails," Mathematics, MDPI, vol. 10(19), pages 1-24, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3677-:d:936007
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    References listed on IDEAS

    as
    1. Opsomer, Jean D., 2000. "Asymptotic Properties of Backfitting Estimators," Journal of Multivariate Analysis, Elsevier, vol. 73(2), pages 166-179, May.
    2. Gonzálo Carreño & Xaviera A. López-Cortés & Carolina Marchant, 2022. "Machine Learning Models to Predict Critical Episodes of Environmental Pollution for PM2.5 and PM10 in Talca, Chile," Mathematics, MDPI, vol. 10(3), pages 1-17, January.
    3. Germán Ibacache-Pulgar & Gilberto Paula & Francisco Cysneiros, 2013. "Semiparametric additive models under symmetric distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 103-121, March.
    4. W.‐Y. Poon & Y. S. Poon, 1999. "Conformal normal curvature and assessment of local influence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 51-61.
    5. Rodrigo Puentes & Carolina Marchant & Víctor Leiva & Jorge I. Figueroa-Zúñiga & Fabrizio Ruggeri, 2021. "Predicting PM2.5 and PM10 Levels during Critical Episodes Management in Santiago, Chile, with a Bivariate Birnbaum-Saunders Log-Linear Model," Mathematics, MDPI, vol. 9(6), pages 1-24, March.
    6. Clécio S. Ferreira & Gilberto A. Paula, 2017. "Estimation and diagnostic for skew-normal partially linear models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(16), pages 3033-3053, December.
    7. R. A. Rigby & D. M. Stasinopoulos, 2005. "Generalized additive models for location, scale and shape," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(3), pages 507-554, June.
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    Cited by:

    1. Hasnain Iftikhar & Josue E. Turpo-Chaparro & Paulo Canas Rodrigues & Javier Linkolk López-Gonzales, 2023. "Forecasting Day-Ahead Electricity Prices for the Italian Electricity Market Using a New Decomposition—Combination Technique," Energies, MDPI, vol. 16(18), pages 1-23, September.
    2. Hasnain Iftikhar & Aimel Zafar & Josue E. Turpo-Chaparro & Paulo Canas Rodrigues & Javier Linkolk López-Gonzales, 2023. "Forecasting Day-Ahead Brent Crude Oil Prices Using Hybrid Combinations of Time Series Models," Mathematics, MDPI, vol. 11(16), pages 1-19, August.
    3. Hasnain Iftikhar & Josue E. Turpo-Chaparro & Paulo Canas Rodrigues & Javier Linkolk López-Gonzales, 2023. "Day-Ahead Electricity Demand Forecasting Using a Novel Decomposition Combination Method," Energies, MDPI, vol. 16(18), pages 1-22, September.

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