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

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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 \(\texttt {CensMixReg}\).

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Acknowledgements

We are grateful to four anonymous referees, the editor and the associate editor for very useful comments and suggestions, which greatly improved this paper. This paper was written while Celso R. B. Cabral was a visiting professor in the Department of Statistics at the University of Campinas, Brazil. Celso R. B. Cabral was supported by CNPq (Grants 167731/2013-0 and 447964/2014-3), and FAPESP-Brazil (Grant 2015/20922-5). V.H. Lachos acknowledges support from FAPESP-Brazil (Grant 2018/05013-7). M.O. Prates was supported by CNPq-Brazil (Grant PQ-305401/2017-7) and FAPEMIG-Brazil (Grant PPM-00532-16). We also thank Luis B. Sanchez from University of São Paulo for his help on an earlier version of the article.

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Authors and Affiliations

  1. Department of Statistics, University of Connecticut, Storrs, CT, 06269, USA

    Víctor H. Lachos & Dipak K. Dey

  2. Departamento de Estatística, Universidade Federal do Amazonas, Av. General Rodrigo Octávio, 6200, Coroado I, CEP 69080-900, Manaus, Amazonas, Brazil

    Celso R. B. Cabral

  3. Departamento de Estatística, Universidade Federal de Minas Gerais, Belo Horizonte, Brazil

    Marcos O. Prates

Authors
  1. Víctor H. Lachos
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  2. Celso R. B. Cabral
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  3. Marcos O. Prates
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  4. Dipak K. Dey
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Corresponding author

Correspondence to Celso R. B. Cabral.

Appendix: Simulation Study 2: bias and RMSE with data generated by the FM-NCR model

Appendix: Simulation Study 2: bias and RMSE with data generated by the FM-NCR model

See Tables 7 and 8.

Table 7 Simulation Study 2: Bias of estimates with data generated by the FM-NCR model
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Table 8 Simulation Study 2: Root mean squared errors (RMSE) of estimates with data generated by the FM-NCR model
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Lachos, V.H., Cabral, C.R.B., Prates, M.O. et al. Flexible regression modeling for censored data based on mixtures of student-t distributions. Comput Stat 34, 123–152 (2019). https://doi.org/10.1007/s00180-018-0856-1

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  • DOI: https://doi.org/10.1007/s00180-018-0856-1

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