Combining Generalized Linear Autoregressive Moving Average and Bootstrap Models for Analyzing Time Series of Respiratory Diseases and Air Pollutants
The generalized linear autoregressive moving-average model (GLARMA) has been used in epidemiology to evaluate the impact of pollutants on health. These effects are quantified through the relative risk (RR) measure, which inference can be based on the asymptotic properties of the maximum likelihood e...
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MDPI AG
2025-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/13/5/859 |
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| author | Ana Julia Alves Camara Valdério Anselmo Reisen Glaura Conceicao Franco Pascal Bondon |
| author_facet | Ana Julia Alves Camara Valdério Anselmo Reisen Glaura Conceicao Franco Pascal Bondon |
| author_sort | Ana Julia Alves Camara |
| collection | DOAJ |
| description | The generalized linear autoregressive moving-average model (GLARMA) has been used in epidemiology to evaluate the impact of pollutants on health. These effects are quantified through the relative risk (RR) measure, which inference can be based on the asymptotic properties of the maximum likelihood estimator. However, for small series, this can be troublesome. This work studies different types of bootstrap confidence intervals (CIs) for the RR. The simulation study revealed that the model parameter related to the data’s autocorrelation could influence the intervals’ coverage. Problems could arise when covariates present an autocorrelation structure. To solve this, using the vector autoregressive (VAR) filter in the covariates is suggested. |
| format | Article |
| id | doaj-art-fd69faff2e3b48d881a0ee2852166cc6 |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-fd69faff2e3b48d881a0ee2852166cc62025-08-20T02:59:00ZengMDPI AGMathematics2227-73902025-03-0113585910.3390/math13050859Combining Generalized Linear Autoregressive Moving Average and Bootstrap Models for Analyzing Time Series of Respiratory Diseases and Air PollutantsAna Julia Alves Camara0Valdério Anselmo Reisen1Glaura Conceicao Franco2Pascal Bondon3Department of Statistics, Federal University of Espirito Santo, Av. Fernando Ferrari, 514, Vitoria 29075-910, BrazilPPGEA (Graduate Program in Environmental Engineering), Federal University of Espirito Santo, Av. Fernando Ferrari, 514, Vitoria 29075-910, BrazilDepartment of Statistics, Federal University of Minas Gerais, Av. Antonio Carlos 6627, Belo Horizonte 31270-901, BrazilLaboratoire des Signaux et Systèmes, CentraleSupélec, CNRS, Université Paris-Saclay, 3 Rue Joliot Curie, 91192 Gif-sur-Yvette, FranceThe generalized linear autoregressive moving-average model (GLARMA) has been used in epidemiology to evaluate the impact of pollutants on health. These effects are quantified through the relative risk (RR) measure, which inference can be based on the asymptotic properties of the maximum likelihood estimator. However, for small series, this can be troublesome. This work studies different types of bootstrap confidence intervals (CIs) for the RR. The simulation study revealed that the model parameter related to the data’s autocorrelation could influence the intervals’ coverage. Problems could arise when covariates present an autocorrelation structure. To solve this, using the vector autoregressive (VAR) filter in the covariates is suggested.https://www.mdpi.com/2227-7390/13/5/859time series of countsINAR modelsinteger-valued datarespiratory diseasesair pollution |
| spellingShingle | Ana Julia Alves Camara Valdério Anselmo Reisen Glaura Conceicao Franco Pascal Bondon Combining Generalized Linear Autoregressive Moving Average and Bootstrap Models for Analyzing Time Series of Respiratory Diseases and Air Pollutants Mathematics time series of counts INAR models integer-valued data respiratory diseases air pollution |
| title | Combining Generalized Linear Autoregressive Moving Average and Bootstrap Models for Analyzing Time Series of Respiratory Diseases and Air Pollutants |
| title_full | Combining Generalized Linear Autoregressive Moving Average and Bootstrap Models for Analyzing Time Series of Respiratory Diseases and Air Pollutants |
| title_fullStr | Combining Generalized Linear Autoregressive Moving Average and Bootstrap Models for Analyzing Time Series of Respiratory Diseases and Air Pollutants |
| title_full_unstemmed | Combining Generalized Linear Autoregressive Moving Average and Bootstrap Models for Analyzing Time Series of Respiratory Diseases and Air Pollutants |
| title_short | Combining Generalized Linear Autoregressive Moving Average and Bootstrap Models for Analyzing Time Series of Respiratory Diseases and Air Pollutants |
| title_sort | combining generalized linear autoregressive moving average and bootstrap models for analyzing time series of respiratory diseases and air pollutants |
| topic | time series of counts INAR models integer-valued data respiratory diseases air pollution |
| url | https://www.mdpi.com/2227-7390/13/5/859 |
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