Abstract
Often, real-life problems require modelling several response variables together. This work analyses a multivariate linear regression model when the data are censored. Censoring distorts the correlation structure of the underlying variables and increases the bias of the usual estimators. Thus, we propose three methods to deal with multivariate data under left censoring, namely Expectation Maximization (EM), Data Augmentation (DA) and Gibbs Sampler with Data Augmentation (GDA). Results from a simulation study show that both DA and GDA estimates are consistent for low and moderate correlation. Under high correlation scenarios, EM estimates present a lower bias.
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Notes
- 1.
The generalization of this study to more than one independent variable is trivial for DA and GDA. However, the computation of the EM estimates may be hindered by the need to obtain the moments of the truncated multivariate distributions.
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Acknowledgements
This work is supported by Fundação Calouste Gulbenkian and the Center for Research and Development in Mathematics and Applications (CIDMA) through the Portuguese Foundation for Science and Technology (FCT—Fundação para a Ciência e a Tecnologia), reference UIDB/04106/2020.
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Sousa, R., Pereira, I., Silva, M.E. (2022). Censored Multivariate Linear Regression Model. In: Bispo, R., Henriques-Rodrigues, L., Alpizar-Jara, R., de Carvalho, M. (eds) Recent Developments in Statistics and Data Science. SPE 2021. Springer Proceedings in Mathematics & Statistics, vol 398. Springer, Cham. https://doi.org/10.1007/978-3-031-12766-3_20
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