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Heteroscedastic nonlinear regression models using asymmetric and heavy tailed two-piece distributions

Author

Listed:
  • Akram Hoseinzadeh

    (Islamic Azad University)

  • Mohsen Maleki

    (University of Isfahan)

  • Zahra Khodadadi

    (Islamic Azad University)

Abstract

In this paper, heteroscedastic nonlinear regression (HNLR) models under the flexible class of two–piece distributions based on the scale mixtures of normal (TP–SMN) family were examined. This novel class of nonlinear regression (NLR) models is a generalization of the well-known heteroscedastic symmetrical nonlinear regression models. The TP–SMN is a rich class of distributions that covers symmetric and asymmetric as well as heavy-tailed distributions. Using the suitable hierarchical representation of the family, the researchers first derived an EM–type algorithm for iteratively computing maximum likelihood (ML) estimates of the parameters. Then, in order to examine the performance of the proposed models and methods, some simulation studies were presented to show the robust aspect of this flexible class against outlying and also atypical data. As the last step, a natural real dataset was fitted under the proposed HNLR models.

Suggested Citation

  • Akram Hoseinzadeh & Mohsen Maleki & Zahra Khodadadi, 2021. "Heteroscedastic nonlinear regression models using asymmetric and heavy tailed two-piece distributions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(3), pages 451-467, September.
    • Handle: RePEc:spr:alstar:v:105:y:2021:i:3:d:10.1007_s10182-020-00384-3
    DOI: 10.1007/s10182-020-00384-3
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    References listed on IDEAS

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    1. Mohsen Maleki & Mohammad Reza Mahmoudi, 2017. "Two-Piece location-scale distributions based on scale mixtures of normal family," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(24), pages 12356-12369, December.
    2. Clécio S. Ferreira & Víctor H. Lachos & Heleno Bolfarine, 2016. "Likelihood-based inference for multivariate skew scale mixtures of normal distributions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(4), pages 421-441, October.
    3. Branco, Márcia D. & Dey, Dipak K., 2001. "A General Class of Multivariate Skew-Elliptical Distributions," Journal of Multivariate Analysis, Elsevier, vol. 79(1), pages 99-113, October.
    4. Mohsen Maleki & Darren Wraith, 2019. "Mixtures of multivariate restricted skew-normal factor analyzer models in a Bayesian framework," Computational Statistics, Springer, vol. 34(3), pages 1039-1053, September.
    5. A. Hajrajabi & M. Maleki, 2019. "Nonlinear semiparametric autoregressive model with finite mixtures of scale mixtures of skew normal innovations," Journal of Applied Statistics, Taylor & Francis Journals, vol. 46(11), pages 2010-2029, August.
    6. Aldo M. Garay & Victor H. Lachos & Heleno Bolfarine & Celso R. B. Cabral, 2017. "Linear censored regression models with scale mixtures of normal distributions," Statistical Papers, Springer, vol. 58(1), pages 247-278, March.
    7. Arellano-Valle, Reinaldo B. & Azzalini, Adelchi & Ferreira, Clécio S. & Santoro, Karol, 2020. "A two-piece normal measurement error model," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    8. Clécio da Silva Ferreira & Víctor H. Lachos & Aldo M. Garay, 2020. "Inference and diagnostics for heteroscedastic nonlinear regression models under skew scale mixtures of normal distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 47(9), pages 1690-1719, June.
    9. Cysneiros, Francisco José A. & Vanegas, Luis Hernando, 2008. "Residuals and their statistical properties in symmetrical nonlinear models," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3269-3273, December.
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    Cited by:

    1. Atefeh Zarei & Zahra Khodadadi & Mohsen Maleki & Karim Zare, 2023. "Robust mixture regression modeling based on two-piece scale mixtures of normal distributions," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 17(1), pages 181-210, March.

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