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Assessment of diagnostic procedures in symmetrical nonlinear regression models

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

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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  • Vanegas, Luis Hernando & Cysneiros, Francisco José A., 2010. "Assessment of diagnostic procedures in symmetrical nonlinear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 1002-1016, April.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:4:p:1002-1016
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    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. 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.
    3. 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.
    4. 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.
    5. Víctor Leiva & Shuangzhe Liu & Lei Shi & Francisco José A. Cysneiros, 2016. "Diagnostics in elliptical regression models with stochastic restrictions applied to econometrics," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(4), pages 627-642, March.
    6. Carlos Eduardo M. Relvas & Gilberto A. Paula, 2016. "Partially linear models with first-order autoregressive symmetric errors," Statistical Papers, Springer, vol. 57(3), pages 795-825, September.
    7. Luis Hernando Vanegas & Gilberto A. Paula, 2017. "Log-symmetric regression models under the presence of non-informative left- or right-censored observations," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(2), pages 405-428, June.
    8. Jin-Guan Lin & Chun-Zheng Cao, 2013. "On estimation of measurement error models with replication under heavy-tailed distributions," Computational Statistics, Springer, vol. 28(2), pages 809-829, April.
    9. 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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