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Influence diagnostics in generalized symmetric linear models


  • Villegas, Cristian
  • Paula, Gilberto A.
  • Cysneiros, Francisco José A.
  • Galea, Manuel


The aim of this paper is to introduce generalized symmetric linear models (GSLMs) in the same sense of generalized linear models (GLMs), in which a link function is defined to establish a relationship between the mean values of symmetric distributions and linear predictors. The class of symmetric distributions contains various distributions with lighter and heavier tails than normal and hence offers a more flexible basis for analyzing symmetric data. An iteratively reweighed least squares (IRLS) algorithm is derived to obtain maximum likelihood estimates. The local influence methodology is applied to study the sensitivity of the maximum likelihood estimates under some usual perturbation schemes, such as case-weight, response variable, continuous explanatory variable and scale parameter perturbations. We also discuss generalized leverage and residual analysis. Finally, an illustration is given in which the methodology developed in this paper is applied to a real data set.

Suggested Citation

  • Villegas, Cristian & Paula, Gilberto A. & Cysneiros, Francisco José A. & Galea, Manuel, 2013. "Influence diagnostics in generalized symmetric linear models," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 161-170.
  • Handle: RePEc:eee:csdana:v:59:y:2013:i:c:p:161-170
    DOI: 10.1016/j.csda.2012.10.012

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    References listed on IDEAS

    1. Manuel Galea & Gilberto Paula & Miguel Uribe-Opazo, 2003. "On influence diagnostic in univariate elliptical linear regression models," Statistical Papers, Springer, vol. 44(1), pages 23-45, January.
    2. Gilberto Paula & Francisco Jose Cysneiros, 2009. "Systematic risk estimation in symmetric models," Applied Economics Letters, Taylor & Francis Journals, vol. 16(2), pages 217-221.
    3. Cysneiros, Francisco José A. & Paula, Gilberto A. & Galea, Manuel, 2007. "Heteroscedastic symmetrical linear models," Statistics & Probability Letters, Elsevier, vol. 77(11), pages 1084-1090, June.
    4. 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.
    5. Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
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    Cited by:

    1. repec:spr:sankhb:v:79:y:2017:i:1:d:10.1007_s13571-016-0116-8 is not listed on IDEAS
    2. 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.
    3. repec:bla:stanee:v:71:y:2017:i:3:p:200-224 is not listed on IDEAS


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