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Maximum likelihood methods in a robust censored errors-in-variables model

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Abstract

We develop a non-standard linear regression analysis by considering that the dependent variable is left censored and also that some of the explanatory variables are measured with additive errors. Our censored measurement error regression model is specified by assuming heavy-tailed distributions for the underlying probabilistic process. Specifically, we focus on assuming a multivariate \(t\) joint distribution for the error terms and the unobserved true covariates. For the model estimation, we consider the maximum likelihood methodology in which we include the estimation of the asymptotic variance of the maximum likelihood estimators. We also develop an EM algorithm to obtain the estimates. The performance of the newly developed methodology is evaluated throughout a simulation study as well as a case study analysis.

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Acknowledgments

We would like to express our gratitude to the editors and two anonymous referees. Their constructive criticisms and suggestions contributed definitively to the improvement of the paper. The research of G. H. M. A. Rocha was partially supported by CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior) of Brazil. The research of R. B. Arellano-Valle was partially supported by Grants FONDECYT 1120121 from Chilean government. R. H. Loschi would like to thank CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico) of the Ministry for Science and Technology of Brazil, grants 301393/2013-3 and 306085/2009-7 for a partial allowance to her researches.

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Authors and Affiliations

  1. Departamento de Estatística, Universidade Federal de Minas Gerais, Belo Horizonte, MG, 31270-901, Brazil

    Gustavo H. M. A. Rocha & Rosangela H. Loschi

  2. Departamento de Estadística, Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Santiago, Chile

    Reinaldo B. Arellano-Valle

Authors
  1. Gustavo H. M. A. Rocha
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  2. Reinaldo B. Arellano-Valle
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  3. Rosangela H. Loschi
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Correspondence to Rosangela H. Loschi.

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Rocha, G.H.M., Arellano-Valle, R.B. & Loschi, R.H. Maximum likelihood methods in a robust censored errors-in-variables model. TEST 24, 857–877 (2015). https://doi.org/10.1007/s11749-015-0439-1

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  • DOI: https://doi.org/10.1007/s11749-015-0439-1

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