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Flexible regression modeling for censored data based on mixtures of student-t distributions

Author

Listed:
  • Víctor H. Lachos

    (University of Connecticut)

  • Celso R. B. Cabral

    (Universidade Federal do Amazonas)

  • Marcos O. Prates

    (Universidade Federal de Minas Gerais)

  • Dipak K. Dey

    (University of Connecticut)

Abstract

In some applications of censored regression models, the distribution of the error terms departs significantly from normality, for instance, in the presence of heavy tails, skewness and/or atypical observation. In this paper we extend the censored linear regression model with normal errors to the case where the random errors follow a finite mixture of Student-t distributions. This approach allows us to model data with great flexibility, accommodating multimodality, heavy tails and also skewness depending on the structure of the mixture components. We develop an analytically tractable and efficient EM-type algorithm for iteratively computing maximum likelihood estimates of the parameters, with standard errors as a by-product. The algorithm has closed-form expressions at the E-step, that rely on formulas for the mean and variance of the truncated Student-t distributions. The efficacy of the method is verified through the analysis of simulated and real datasets. The proposed algorithm and methods are implemented in the new R package $$\texttt {CensMixReg}$$ CensMixReg .

Suggested Citation

  • Víctor H. Lachos & Celso R. B. Cabral & Marcos O. Prates & Dipak K. Dey, 2019. "Flexible regression modeling for censored data based on mixtures of student-t distributions," Computational Statistics, Springer, vol. 34(1), pages 123-152, March.
    • Handle: RePEc:spr:compst:v:34:y:2019:i:1:d:10.1007_s00180-018-0856-1
    DOI: 10.1007/s00180-018-0856-1
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    References listed on IDEAS

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    4. Aldo M. Garay & Heleno Bolfarine & Victor H. Lachos & Celso R.B. Cabral, 2015. "Bayesian analysis of censored linear regression models with scale mixtures of normal distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(12), pages 2694-2714, December.
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