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

Gustavo H. M. A. Rocha ^[2] ; Reinaldo B. Arellano-Valle ^[1] ; Rosangela H. Loschi ^[2]
1. [1] Pontificia Universidad Católica de Chile
  
  Pontificia Universidad Católica de Chile
  
  Santiago, Chile
2. [2] Universidade Federal de Minas
Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 24, Nº. 4, 2015, págs. 857-877
Idioma: inglés
DOI: 10.1007/s11749-015-0439-1
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Resumen
- 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.