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On estimation of a heteroscedastic measurement error model under heavy-tailed distributions

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  • Cao, Chun-Zheng
  • Lin, Jin-Guan
  • Zhu, Xiao-Xin

Abstract

It is common in epidemiology and other fields that the analyzing data is collected with error-prone observations and the variances of the measurement errors change across observations. Heteroscedastic measurement error (HME) models have been developed for such data. This paper extends the structural HME model to situations in which the observations jointly follow scale mixtures of normal (SMN) distribution. We develop the EM algorithm to compute the maximum likelihood estimates for the model with and without equation error respectively, and derive closed forms of asymptotic variances. We also conduct simulations to verify the effective of the EM estimates and confirm their robust behaviors based on heavy-tailed SMN distributions. A practical application is reported for the data from the WHO MONICA Project on cardiovascular disease.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:2:p:438-448
    DOI: 10.1016/j.csda.2011.08.011
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    References listed on IDEAS

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    1. 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.
    2. 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.
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    Cited by:

    1. 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.
    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.

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