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Influence diagnostics for Grubbs’s model with asymmetric heavy-tailed distributions

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  • Camila Zeller
  • Victor Lachos
  • Filidor Labra

Abstract

Grubbs’s model (Grubbs, Encycl Stat Sci 3:42–549, 1983 ) is used for comparing several measuring devices, and it is common to assume that the random terms have a normal (or symmetric) distribution. In this paper, we discuss the extension of this model to the class of scale mixtures of skew-normal distributions. Our results provide a useful generalization of the symmetric Grubbs’s model (Osorio et al., Comput Stat Data Anal, 53:1249–1263, 2009 ) and the asymmetric skew-normal model (Montenegro et al., Stat Pap 51:701–715, 2010 ). We discuss the EM algorithm for parameter estimation and the local influence method (Cook, J Royal Stat Soc Ser B, 48:133–169, 1986 ) for assessing the robustness of these parameter estimates under some usual perturbation schemes. The results and methods developed in this paper are illustrated with a numerical example. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Camila Zeller & Victor Lachos & Filidor Labra, 2014. "Influence diagnostics for Grubbs’s model with asymmetric heavy-tailed distributions," Statistical Papers, Springer, vol. 55(3), pages 671-690, August.
    • Handle: RePEc:spr:stpapr:v:55:y:2014:i:3:p:671-690
    DOI: 10.1007/s00362-013-0519-9
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    References listed on IDEAS

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    1. Lourdes Montenegro & Víctor Lachos & Heleno Bolfarine, 2010. "Inference for a skew extension of the Grubbs model," Statistical Papers, Springer, vol. 51(3), pages 701-715, September.
    2. de Castro, Mario & Galea-Rojas, Manuel & Bolfarine, Heleno, 2007. "Local influence assessment in heteroscedastic measurement error models," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 1132-1142, October.
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    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.
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    8. Lounasheimo, Antton, 1999. "The Impact of Human Capital on Economic Growth," Discussion Papers 673, The Research Institute of the Finnish Economy.
    9. Osorio, Felipe & Paula, Gilberto A. & Galea, Manuel, 2009. "On estimation and influence diagnostics for the Grubbs' model under heavy-tailed distributions," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1249-1263, February.
    10. Lee, Sik-Yum & Xu, Liang, 2004. "Influence analyses of nonlinear mixed-effects models," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 321-341, March.
    11. C. B. Zeller & V. H. Lachos & F. E. Vilca-Labra, 2011. "Local influence analysis for regression models with scale mixtures of skew-normal distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(2), pages 343-368, October.
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    2. Chunzheng Cao & Mengqian Chen & Yahui Wang & Jian Qing Shi, 2018. "Heteroscedastic replicated measurement error models under asymmetric heavy-tailed distributions," Computational Statistics, Springer, vol. 33(1), pages 319-338, March.
    3. Zeinolabedin Najafi & Karim Zare & Mohammad Reza Mahmoudi & Soheil Shokri & Amir Mosavi, 2022. "Inference and Local Influence Assessment in a Multifactor Skew-Normal Linear Mixed Model," Mathematics, MDPI, vol. 10(15), pages 1-21, August.
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    5. Chunzheng Cao & Yahui Wang & Jian Qing Shi & Jinguan Lin, 2018. "Measurement Error Models for Replicated Data Under Asymmetric Heavy-Tailed Distributions," Computational Economics, Springer;Society for Computational Economics, vol. 52(2), pages 531-553, August.

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