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Residuals and their statistical properties in symmetrical nonlinear models

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

Abstract

In this work we present theoretical details of a general residual for symmetric nonlinear regression models. This class of models includes all symmetric continuous distributions such as normal, Student-t, Pearson VII, power exponential and logistic. Such regression models are used for the analysis of data sets containing influential or outlying observations, that can significantly influence inferential conclusions. On the basis of expansions of Cox and Snell [Cox, D.R., Snell, E.J., 1968. A general definition of residuals. Journal of the Royal Statistical Society B 30, 248-275], we calculate first and second moments of a general definition of a residual for symmetrical nonlinear regression models. Also, the statistical properties of some proposed residuals are studied using Monte Carlo simulations for the Michaelis-Menten model, frequently used in chemical and biological experiments.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:18:p:3269-3273
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    References listed on IDEAS

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    1. 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.
    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.
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    Cited by:

    1. 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.
    2. 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.
    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. 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.
    6. 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.
    7. 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.

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