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Estimation and Influence Diagnostics for the Multivariate Linear Regression Models with Skew Scale Mixtures of Normal Distributions

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  • Graciliano M. S. Louredo

    (Universidade Federal de Juiz de Fora)

  • Camila B. Zeller

    (Universidade Federal de Juiz de Fora)

  • Clécio S. Ferreira

    (Universidade Federal de Juiz de Fora)

Abstract

In this paper, we present recent results in the context of multivariate linear regression models considering that random errors follow multivariate skew scale mixtures of normal distributions. This class of distributions includes the scale mixtures of multivariate normal distributions, as special cases, and provides flexibility in capturing a wide variety of asymmetric behaviors. We implemented the algorithm ECM (Expectation/Conditional Maximization) and we obtained closed-form expressions for all the estimators of the parameters of the proposed model. Inspired by the ECM algorithm, we have developed an influence diagnostics for detecting influential observations to investigate the sensitivity of the maximum likelihood estimators. To examine the performance and the usefulness of the proposed methodology, we present simulation studies and analyze a real dataset.

Suggested Citation

  • Graciliano M. S. Louredo & Camila B. Zeller & Clécio S. Ferreira, 2022. "Estimation and Influence Diagnostics for the Multivariate Linear Regression Models with Skew Scale Mixtures of Normal Distributions," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 204-242, May.
    • Handle: RePEc:spr:sankhb:v:84:y:2022:i:1:d:10.1007_s13571-021-00257-y
    DOI: 10.1007/s13571-021-00257-y
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    References listed on IDEAS

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    1. Hong‐Tu Zhu & Sik‐Yum Lee, 2001. "Local influence for incomplete data models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(1), pages 111-126.
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    7. Clécio S. Ferreira & Víctor H. Lachos & Heleno Bolfarine, 2016. "Likelihood-based inference for multivariate skew scale mixtures of normal distributions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(4), pages 421-441, October.
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    9. C. B. Zeller & V. H. Lachos & F. E. Vilca-Labra, 2011. "Local influence analysis for regression models with scale mixtures of skew-normal distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(2), pages 343-368, October.
    10. M. Qamarul Islam & Fetih Yildirim & Mehmet Yazici, 2014. "Inference in multivariate linear regression models with elliptically distributed errors," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(8), pages 1746-1766, August.
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    1. Baishuai Zuo & Narayanaswamy Balakrishnan & Chuancun Yin, 2023. "An analysis of multivariate measures of skewness and kurtosis of skew-elliptical distributions," Papers 2311.18176, arXiv.org.

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