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Multivariate measurement error models using finite mixtures of skew-Student t distributions

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  • Cabral, Celso Rômulo Barbosa
  • Lachos, Víctor Hugo
  • Zeller, Camila Borelli

Abstract

In regression models, the classical assumption of normal distribution of the random observational errors is often violated, masking some important features of the variability present in the data. Some practical actions to solve the problem, like transformation of variables to achieve normality, are often of doubtful utility. In this work we present a proposal to deal with this issue in the context of the simple linear regression model when both the response and the explanatory variable are observed with error. In such models, the experimenter observes a surrogate variable instead of the covariate of interest. We extend the classical normal model by jointly modeling the unobserved covariate and the random errors by a finite mixture of a skewed version of the Student t distribution. This approach allows us to model data with great flexibility, accommodating skewness, heavy tails and multi-modality. We develop a simple EM-type algorithm to perform maximum likelihood inference of the parameters of the proposed model, and compare the efficiency of our method with some competitors through the analysis of some artificial and real data.

Suggested Citation

  • Cabral, Celso Rômulo Barbosa & Lachos, Víctor Hugo & Zeller, Camila Borelli, 2014. "Multivariate measurement error models using finite mixtures of skew-Student t distributions," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 179-198.
  • Handle: RePEc:eee:jmvana:v:124:y:2014:i:c:p:179-198
    DOI: 10.1016/j.jmva.2013.10.017
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    References listed on IDEAS

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    5. Sylvia Richardson & Laurent Leblond & Isabelle Jaussent & Peter J. Green, 2002. "Mixture models in measurement error problems, with reference to epidemiological studies," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 165(3), pages 549-566, October.
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    7. Cabral, Celso Rômulo Barbosa & Lachos, Víctor Hugo & Prates, Marcos O., 2012. "Multivariate mixture modeling using skew-normal independent distributions," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 126-142, January.
    8. Arellano-Valle, Reinaldo B. & Genton, Marc G., 2005. "On fundamental skew distributions," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 93-116, September.
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    Cited by:

    1. Clécio S. Ferreira & Víctor H. Lachos & Heleno Bolfarine, 2016. "Likelihood-based inference for multivariate skew scale mixtures of normal distributions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(4), pages 421-441, October.
    2. Graciliano M. S. Louredo & Camila B. Zeller & Clécio S. Ferreira, 2022. "Estimation and Influence Diagnostics for the Multivariate Linear Regression Models with Skew Scale Mixtures of Normal Distributions," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 204-242, May.
    3. O’Hagan, Adrian & Murphy, Thomas Brendan & Gormley, Isobel Claire & McNicholas, Paul D. & Karlis, Dimitris, 2016. "Clustering with the multivariate normal inverse Gaussian distribution," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 18-30.

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