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An EM algorithm for estimating the parameters of the multivariate skew-normal distribution with censored responses

Author

Listed:
  • Christian E. Galarza

    (Escuela Superior Politécnica del Litoral, ESPOL)

  • Larissa A. Matos

    (Universidade Estadual de Campinas)

  • Victor H. Lachos

    (University of Connecticut)

Abstract

Limited or censored data are collected in many studies. This occurs for many reasons in several practical situations, such as limitations in measuring equipment or from an experimental design. Consequently, the true value is recorded only if it falls within an interval range so that the responses can be either left, interval, or right-censored. Missing values can be seen just as a particular case. Linear and nonlinear regression models are routinely used to analyze these types of data. Most of these models are based on the normality assumption for the error term. However, such analyses might not provide robust inference when the normality assumption (or symmetry) is questionable. The need for asymmetric distributions for the random errors motivates us to develop a likelihood-based inference for linear models with censored responses based on the multivariate skew-normal distribution, where the missing/censoring mechanism is assumed to be “missing at random” (MAR). The proposed EM-type algorithm for maximum likelihood estimation uses closed-form expressions at the E-step based on formulas for the mean and variance of a truncated multivariate skew-normal distribution, available in the R package MomTrunc. Three datasets with censored and/or missing observations are analyzed and discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metron:v:80:y:2022:i:2:d:10.1007_s40300-021-00227-4
    DOI: 10.1007/s40300-021-00227-4
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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. A. Azzalini & A. Capitanio, 1999. "Statistical applications of the multivariate skew normal distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 579-602.
    3. 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.
    4. 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.
    5. A. Capitanio & A. Azzalini & E. Stanghellini, 2003. "Graphical models for skew‐normal variates," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(1), pages 129-144, March.
    6. Jun Li & Daniel R. Jeske, 2009. "Maximum likelihood estimators of clock offset and skew under exponential delays," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(4), pages 506-507, July.
    7. Jun Li & Daniel R. Jeske, 2009. "Maximum likelihood estimators of clock offset and skew under exponential delays," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(4), pages 445-459, July.
    8. 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.
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    Cited by:

    1. 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).

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