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Assessment of diagnostic procedures in symmetrical nonlinear regression models

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  • Vanegas, Luis Hernando
  • Cysneiros, Francisco José A.
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    Abstract

    The aim of this paper is to derive diagnostic procedures based on case-deletion model for symmetrical nonlinear regression models, which complements Galea et al. (2005) that developed local influence diagnostics under some perturbation schemes. This class of models includes all symmetric continuous distributions for errors covering both light- and heavy-tailed distributions such as Student-t, logistic-I and -II, power exponential, generalized Student-t, generalized logistic and contaminated normal, among others. Thus, these models can be checked for robustness to outliers in the response variable and diagnostic methods may be a useful tool for an appropriate choice. First, an iterative process for the parameter estimation as well as some inferential results are presented. Besides, we present the results of a simulation study in which the characteristics of heavy-tailed models are evaluated in the presence of outliers. Then, we derive some diagnostic measures such as Cook distance, W-K statistic, one-step approach and likelihood displacement, generalizing results obtained for normal nonlinear regression models. Also, we present simulation studies that illustrate the behavior of diagnostic measures proposed. Finally, we consider two real data sets previously analyzed under normal nonlinear regression models. The diagnostic analysis indicates that a Student-t nonlinear regression model seems to fit the data better than the normal nonlinear regression model as well as other symmetrical nonlinear models in the sense of robustness against extreme observations.

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    File URL: http://www.sciencedirect.com/science/article/B6V8V-4XHVGWJ-1/2/4353bc9fecea8b9d103a3319303bf78a
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    Bibliographic Info

    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 54 (2010)
    Issue (Month): 4 (April)
    Pages: 1002-1016

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    Handle: RePEc:eee:csdana:v:54:y:2010:i:4:p:1002-1016

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    Web page: http://www.elsevier.com/locate/csda

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    References

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    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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    1. Wei, Wen Hsiang & Fung, Wing Kam, 1999. "The mean-shift outlier model in general weighted regression and its applications," Computational Statistics & Data Analysis, Elsevier, vol. 30(4), pages 429-441, June.
    2. Galea, Manuel & Paula, Gilberto A. & Cysneiros, Francisco José A., 2005. "On diagnostics in symmetrical nonlinear models," Statistics & Probability Letters, Elsevier, vol. 73(4), pages 459-467, July.
    3. Sun, Rui-Bo & Wei, Bo-Cheng, 2004. "On influence assessment for LAD regression," Statistics & Probability Letters, Elsevier, vol. 67(2), pages 97-110, April.
    4. 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.
    5. Tang, Nian-Sheng & Wei, Bo-Cheng & Wang, Xue-Ren, 2000. "Influence diagnostics in nonlinear reproductive dispersion models," Statistics & Probability Letters, Elsevier, vol. 46(1), pages 59-68, January.
    6. Cordeiro, Gauss M. & Ferrari, Silvia L. P. & Uribe-Opazo, Miguel A. & Vasconcellos, Klaus L. P., 2000. "Corrected maximum-likelihood estimation in a class of symmetric nonlinear regression models," Statistics & Probability Letters, Elsevier, vol. 46(4), pages 317-328, February.
    7. Cysneiros, Francisco Jose A. & Paula, Gilberto A., 2005. "Restricted methods in symmetrical linear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 49(3), pages 689-708, June.
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    Cited by:
    1. 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.
    2. Garay, Aldo M. & Hashimoto, Elizabeth M. & Ortega, Edwin M.M. & Lachos, Víctor H., 2011. "On estimation and influence diagnostics for zero-inflated negative binomial regression models," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1304-1318, March.
    3. 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.
    4. Cao, Chun-Zheng & Lin, Jin-Guan & Zhu, Xiao-Xin, 2012. "On estimation of a heteroscedastic measurement error model under heavy-tailed distributions," Computational Statistics & Data Analysis, Elsevier, vol. 56(2), pages 438-448.
    5. 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.

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