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Heteroscedastic nonlinear regression models based on scale mixtures of skew-normal distributions

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  • Lachos, Victor H.
  • Bandyopadhyay, Dipankar
  • Garay, Aldo M.

Abstract

An extension of some standard likelihood based procedures to heteroscedastic nonlinear regression models under scale mixtures of skew-normal (SMSN) distributions is developed. We derive a simple EM-type algorithm for iteratively computing maximum likelihood (ML) estimates and the observed information matrix is derived analytically. Simulation studies demonstrate the robustness of this flexible class against outlying and influential observations, as well as nice asymptotic properties of the proposed EM-type ML estimates. Finally, the methodology is illustrated using an ultrasonic calibration data.

Suggested Citation

  • Lachos, Victor H. & Bandyopadhyay, Dipankar & Garay, Aldo M., 2011. "Heteroscedastic nonlinear regression models based on scale mixtures of skew-normal distributions," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1208-1217, August.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:8:p:1208-1217
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    References listed on IDEAS

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    1. Jamshidian, Mortaza, 1999. "Adaptive Robust Regression by Using a Nonlinear Regression Program," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 4(i06).
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    7. Xie, Feng-Chang & Wei, Bo-Cheng & Lin, Jin-Guan, 2009. "Homogeneity diagnostics for skew-normal nonlinear regression models," Statistics & Probability Letters, Elsevier, vol. 79(6), pages 821-827, March.
    8. 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:

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    2. M. Teimourian & T. Baghfalaki & M. Ganjali & D. Berridge, 2015. "Joint modeling of mixed skewed continuous and ordinal longitudinal responses: a Bayesian approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(10), pages 2233-2256, October.
    3. Hu, Hao & Yao, Weixin & Wu, Yichao, 2017. "The robust EM-type algorithms for log-concave mixtures of regression models," Computational Statistics & Data Analysis, Elsevier, vol. 111(C), pages 14-26.
    4. Luis Vanegas & Gilberto Paula, 2015. "A semiparametric approach for joint modeling of median and skewness," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(1), pages 110-135, March.
    5. Zareifard, Hamid & Jafari Khaledi, Majid, 2013. "Non-Gaussian modeling of spatial data using scale mixing of a unified skew Gaussian process," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 16-28.

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