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

Author

Listed:
  • Gustavo Rocha
  • Reinaldo Arellano-Valle
  • Rosangela Loschi

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 $$t$$ 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. Copyright Sociedad de Estadística e Investigación Operativa 2015

Suggested Citation

  • Gustavo Rocha & Reinaldo Arellano-Valle & Rosangela Loschi, 2015. "Maximum likelihood methods in a robust censored errors-in-variables model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(4), pages 857-877, December.
    • Handle: RePEc:spr:testjl:v:24:y:2015:i:4:p:857-877
    DOI: 10.1007/s11749-015-0439-1
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    References listed on IDEAS

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    1. Arellano-Valle, R.B. & Ozan, S. & Bolfarine, H. & Lachos, V.H., 2005. "Skew normal measurement error models," Journal of Multivariate Analysis, Elsevier, vol. 96(2), pages 265-281, October.
    2. Arellano-Valle, Reinaldo B. & Bolfarine, Heleno, 1995. "On some characterizations of the t-distribution," Statistics & Probability Letters, Elsevier, vol. 25(1), pages 79-85, October.
    3. A. Colin Cameron & Pravin K. Trivedi, 2010. "Microeconometrics Using Stata, Revised Edition," Stata Press books, StataCorp LP, number musr, March.
    4. Wang, Liqun, 1998. "Estimation of censored linear errors-in-variables models," Journal of Econometrics, Elsevier, vol. 84(2), pages 383-400, June.
    5. Reinaldo Arellano-Valle & Luis Castro & Graciela González-Farías & Karla Muñoz-Gajardo, 2012. "Student-t censored regression model: properties and inference," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 21(4), pages 453-473, November.
    6. Lin, Tsung I. & Ho, Hsiu J. & Chen, Chiang L., 2009. "Analysis of multivariate skew normal models with incomplete data," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2337-2351, November.
    7. Wang, Liqun, 2002. "A simple adjustment for measurement errors in some limited dependent variable models," Statistics & Probability Letters, Elsevier, vol. 58(4), pages 427-433, July.
    8. Yulia V. Marchenko & Marc G. Genton, 2012. "A Heckman Selection- t Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 304-317, March.
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    Cited by:

    1. Larissa A. Matos & Luis M. Castro & Víctor H. Lachos, 2016. "Censored mixed-effects models for irregularly observed repeated measures with applications to HIV viral loads," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(4), pages 627-653, December.

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