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Likelihood-based inference for the multivariate skew-t regression with censored or missing responses

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  • Valeriano, Katherine A.L.
  • Galarza, Christian E.
  • Matos, Larissa A.
  • Lachos, Victor H.

Abstract

Skew-t regression models have been widely used to model and analyze asymmetric heavy-tailed data. Moreover, observations in this kind of data can be missing or subject to some upper and/or lower detection limits because of the restriction of the experimental apparatus. We propose a novel robust regression model for multiple censored or missing data based on the multivariate skew-t distribution for such data structures. This approach allows us to model data with great flexibility, simultaneously accommodating heavy tails and skewness. We develop an analytically simple yet efficient EM-type algorithm to conduct maximum likelihood estimation of the parameters. The algorithm has closed-form expressions at the E-step that rely on formulas for the mean and variance of truncated multivariate Student’s-t, skew-t, and extended skew-t distributions. Furthermore, a general information-based method for approximating the asymptotic covariance matrix of the estimators is also presented. Results obtained from the analysis of both simulated and real datasets are reported to demonstrate the effectiveness of the proposed method.

Suggested Citation

  • Valeriano, Katherine A.L. & Galarza, Christian E. & Matos, Larissa A. & Lachos, Victor H., 2023. "Likelihood-based inference for the multivariate skew-t regression with censored or missing responses," Journal of Multivariate Analysis, Elsevier, vol. 196(C).
    • Handle: RePEc:eee:jmvana:v:196:y:2023:i:c:s0047259x23000209
    DOI: 10.1016/j.jmva.2023.105174
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    References listed on IDEAS

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    1. Reinaldo B. Arellano-Valle & Marc G. Genton, 2010. "Multivariate extended skew-t distributions and related families," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 201-234.
    2. Thalita do Bem Mattos & Aldo M. Garay & Victor H. Lachos, 2018. "Likelihood-based inference for censored linear regression models with scale mixtures of skew-normal distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(11), pages 2039-2066, August.
    3. Cabral, Celso Rômulo Barbosa & Lachos, Víctor Hugo & Prates, Marcos O., 2012. "Multivariate mixture modeling using skew-normal independent distributions," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 126-142, January.
    4. Larissa A. Matos & Víctor H. Lachos & Tsung-I Lin & Luis M. Castro, 2019. "Heavy-tailed longitudinal regression models for censored data: a robust parametric approach," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 844-878, September.
    5. Arellano-Valle, Reinaldo B. & Genton, Marc G., 2005. "On fundamental skew distributions," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 93-116, September.
    6. Christian E. Galarza & Larissa A. Matos & Victor H. Lachos, 2022. "An EM algorithm for estimating the parameters of the multivariate skew-normal distribution with censored responses," METRON, Springer;Sapienza Università di Roma, vol. 80(2), pages 231-253, August.
    7. Francisco H. C. Alencar & Christian E. Galarza & Larissa A. Matos & Victor H. Lachos, 2022. "Finite mixture modeling of censored and missing data using the multivariate skew-normal distribution," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(3), pages 521-557, September.
    8. Christian E. Galarza & Tsung-I Lin & Wan-Lun Wang & Víctor H. Lachos, 2021. "On moments of folded and truncated multivariate Student-t distributions based on recurrence relations," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(6), pages 825-850, August.
    9. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389, May.
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