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Additive partial linear models with autoregressive symmetric errors and its application to the hospitalizations for respiratory diseases

Author

Listed:
  • Shu Wei Chou-Chen

    (Universidad de Costa Rica)

  • Rodrigo A. Oliveira

    (Tribunal Regional do Trabalho da 18ª Região)

  • Irina Raicher

    (Clinics Hospital of the University of São Paulo Medical School
    Hospital Israelita Albert Einstein)

  • Gilberto A. Paula

    (Universidade de São Paulo)

Abstract

Additive partial linear models with symmetric autoregressive errors of order p are proposed in this paper for modeling time series data. Specifically, we apply this model class to explain the weekly hospitalization for respiratory diseases in Sorocaba, São Paulo, Brazil, by incorporating climate and pollution as covariates, trend and seasonality. The main feature of this model class is its capability of considering a set of explanatory variables with linear and nonlinear structures, which allows, for example, to model jointly trend and seasonality of a time series with additive functions for the nonlinear explanatory variables and a predictor to accommodate discrete and linear explanatory variables. Additionally, the conditional symmetric errors allow the possibility of fitting data with high correlation order, as well as error distributions with heavier or lighter tails than the normal ones. We present the model class and a novel iterative process is derived by combining a P-GAM type algorithm with a quasi-Newton procedure for the parameter estimation. The inferential results, diagnostic procedures, including conditional quantile residual analysis and local influence analysis for sensitivity, are discussed. Simulation studies are performed to assess finite sample properties of parametric and nonparametric estimators. Finally, the data set analysis and concluding remarks are given.

Suggested Citation

  • Shu Wei Chou-Chen & Rodrigo A. Oliveira & Irina Raicher & Gilberto A. Paula, 2024. "Additive partial linear models with autoregressive symmetric errors and its application to the hospitalizations for respiratory diseases," Statistical Papers, Springer, vol. 65(8), pages 5145-5166, October.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:8:d:10.1007_s00362-024-01590-w
    DOI: 10.1007/s00362-024-01590-w
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    References listed on IDEAS

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    3. Rodrigo A. Oliveira & Gilberto A. Paula, 2021. "Additive models with autoregressive symmetric errors based on penalized regression splines," Computational Statistics, Springer, vol. 36(4), pages 2435-2466, December.
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