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Linear regression models with slash-elliptical errors

Author

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  • Alcantara, Izabel Cristina
  • Cysneiros, Francisco José A.

Abstract

We propose a linear regression model with slash-elliptical errors. The slash-elliptical distribution with parameter q is defined as the ratio of two independent random variables Z and U1q, where Z has elliptical distribution and U has uniform distribution in (0,1). The main feature of the slash-elliptical distribution is to have greater flexibility in the degree of kurtosis when compared to the elliptical distributions. Other advantages of this distribution are the properties of symmetry, heavy tails and the inclusion of the elliptical family as a limit case when q→∞. We develop the methodology of estimation, hypothesis testing, generalized leverage and residuals for the proposed model. In the analysis of local influence, we also develop the diagnostic measures based on the likelihood displacement under the some perturbation schemes. Finally, we present a real example where slash-Student-t model is more stable than other considered models.

Suggested Citation

  • Alcantara, Izabel Cristina & Cysneiros, Francisco José A., 2013. "Linear regression models with slash-elliptical errors," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 153-164.
    • Handle: RePEc:eee:csdana:v:64:y:2013:i:c:p:153-164
    DOI: 10.1016/j.csda.2013.02.029
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    References listed on IDEAS

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    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. Bo‐Cheng Wei & Yue‐Qing Hu & Wing‐Kam Fung, 1998. "Generalized Leverage and its Applications," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 25(1), pages 25-37, March.
    3. Paula, Gilberto A. & Medeiros, Marcio & Vilca-Labra, Filidor E., 2009. "Influence diagnostics for linear models with first-order autoregressive elliptical errors," Statistics & Probability Letters, Elsevier, vol. 79(3), pages 339-346, February.
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    5. Manuel Galea & Heleno Bolfarine & Filidor Vilcalabra, 2002. "Influence diagnostics for the structural errors-in-variables model under the Student-t distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 29(8), pages 1191-1204.
    6. 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.
    7. Arslan, Olcay, 2008. "An alternative multivariate skew-slash distribution," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2756-2761, November.
    8. Gómez, Héctor W. & Quintana, Fernando A. & Torres, Francisco J., 2007. "A new family of slash-distributions with elliptical contours," Statistics & Probability Letters, Elsevier, vol. 77(7), pages 717-725, April.
    9. 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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