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Homogeneity diagnostics for skew-normal nonlinear regression models

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  • Xie, Feng-Chang
  • Wei, Bo-Cheng
  • Lin, Jin-Guan

Abstract

Regression model with skew-normal errors provides useful extension for ordinary normal regression models when the data set under consideration involves asymmetric outcomes. On the other hand, the homogeneity of variances (if they exist) is a standard assumption in skew-normal nonlinear regression models. However, this assumption is not necessarily appropriate. This paper is devoted to the score tests for homogeneity of scalar parameter and skewness parameter in skew-normal nonlinear regression models, which are included in the variance. The properties of score tests are investigated through Monte Carlo simulations. The test methods are illustrated with a numerical example.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:6:p:821-827
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    References listed on IDEAS

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    1. Azzalini, Adelchi, 2022. "An overview on the progeny of the skew-normal family— A personal perspective," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    2. Xu, Dengke & Zhang, Zhongzhan, 2013. "A semiparametric Bayesian approach to joint mean and variance models," Statistics & Probability Letters, Elsevier, vol. 83(7), pages 1624-1631.
    3. Cancho, Vicente G. & Dey, Dipak K. & Lachos, Victor H. & Andrade, Marinho G., 2011. "Bayesian nonlinear regression models with scale mixtures of skew-normal distributions: Estimation and case influence diagnostics," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 588-602, January.
    4. Vanegas, Luis Hernando & Rondón, Luz Marina & Cysneiros, Francisco José A., 2012. "Diagnostic procedures in Birnbaum–Saunders nonlinear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1662-1680.
    5. 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.
    6. Camila Zeller & Rignaldo Carvalho & Victor Lachos, 2012. "On diagnostics in multivariate measurement error models under asymmetric heavy-tailed distributions," Statistical Papers, Springer, vol. 53(3), pages 665-683, August.

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