Abstract
This paper proposes partially linear models with random errors following p-order autoregressive (AR) with skew-normal errors. The maximum likelihood estimators are derived from the Expectation-Maximization algorithm, which have analytic expressions for the M and E-steps. The estimation of the effective degrees of freedom concerning the nonparametric component are obtained based on a linear smoother. The conditional quantile residuals are used for the construction of simulated confidence bands to assess departures from the error assumptions, as well as autocorrelation and partial autocorrelation graphs are considered to check adequacy of the AR error structure. A simulation study is carried out to evaluate the efficiency of the EM algorithm. Finally, the methodology is illustrated by a real data set on cardiovascular mortality.
Funding Statement
The first author was supported by FAPEMIG (Fundação de Amparo à Pesquisa do Estado de Minas Gerais) Grant CEX-APQ-00409-22 and CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico) Grant 302666/2022-2.
The second author was supported by FAPESP (Fundação de Amparo à Pesquisa do Estado de São Paulo) Grant 2018/04654-9.
The third author was supported by CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico) Grant 305189/2018-2.
Acknowledgments
We thank the Associate Editor and referees for their helpful comments and suggestions, leading to the improvement of the paper.
Heleno Bolfarine has a great contribution in the area of asymmetric models. His first papers were published in 2005, one about linear mixed models (Arellano-Valle et al., 2005) (one of the most cited) and another about measurement error models (Arellano-Valle et al., 2005). In total, Heleno published about 47 papers involving asymmetry, considering different models, such as item response theory (Bazán, Bolfarine and Branco, 2006), linear calibration (Figueiredo et al., 2008), classes of skew distributions family (Ferreira, Bolfarine and Lachos, 2011), among others. This work was inpired by Heleno’s hungry for knowledge, which included the use of asymmetric models.
Citation
Clécio da Silva Ferreira. Michel H. Montoril. Gilberto A. Paula. "Partially linear models with p-order autoregressive skew-normal errors." Braz. J. Probab. Stat. 36 (4) 792 - 806, December 2022. https://doi.org/10.1214/22-BJPS556
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