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Heteroscedastic replicated measurement error models under asymmetric heavy-tailed distributions

Author

Listed:
  • Chunzheng Cao

    (Nanjing University of Information Science and Technology)

  • Mengqian Chen

    (Nanjing University of Information Science and Technology)

  • Yahui Wang

    (Nanjing University of Information Science and Technology)

  • Jian Qing Shi

    (Newcastle University)

Abstract

We propose a heteroscedastic replicated measurement error model based on the class of scale mixtures of skew-normal distributions, which allows the variances of measurement errors to vary across subjects. We develop EM algorithms to calculate maximum likelihood estimates for the model with or without equation error. An empirical Bayes approach is applied to estimate the true covariate and predict the response. Simulation studies show that the proposed models can provide reliable results and the inference is not unduly affected by outliers and distribution misspecification. The method has also been used to analyze a real data of plant root decomposition.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:compst:v:33:y:2018:i:1:d:10.1007_s00180-017-0720-8
    DOI: 10.1007/s00180-017-0720-8
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. A. Azzalini & A. Capitanio, 1999. "Statistical applications of the multivariate skew normal distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 579-602.
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    5. Basso, Rodrigo M. & Lachos, Víctor H. & Cabral, Celso Rômulo Barbosa & Ghosh, Pulak, 2010. "Robust mixture modeling based on scale mixtures of skew-normal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 2926-2941, December.
    6. V. Lachos & T. Angolini & C. Abanto-Valle, 2011. "On estimation and local influence analysis for measurement errors models under heavy-tailed distributions," Statistical Papers, Springer, vol. 52(3), pages 567-590, August.
    7. Vicente Cancho & Víctor Lachos & Edwin Ortega, 2010. "A nonlinear regression model with skew-normal errors," Statistical Papers, Springer, vol. 51(3), pages 547-558, September.
    8. 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.
    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.
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    11. Camila Zeller & Rignaldo Carvalho & Victor Lachos, 2012. "On diagnostics in multivariate measurement error models under asymmetric heavy-tailed distributions," Statistical Papers, Springer, vol. 53(3), pages 665-683, August.
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