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<p>Scale mixtures of skew-normal distributions form a class of asymmetric thick-tailed distributions that include skew-normal, skew-t, skew-contaminated normal, and the entire family of scale mixtures of normal distributions as special cases. This paper proposes an interval-censored linear regression model based on the class of scale mixtures of skew-normal distributions, providing an appealing, robust alternative to the usual Gaussian assumption in censored regression models. A novel Expectation/Conditional Maximization Either algorithm is proposed for maximum likelihood estimation, with analytical expressions at the E-step, as opposed to Monte Carlo simulations. These expressions rely on formulas for the mean and variance of truncated scale mixtures of skew-normal distributions that can be computed using the <Emphasis FontCategory="NonProportional">MomTrunc</Emphasis> <Emphasis FontCategory="NonProportional">R</Emphasis> package. The proposed methodology is illustrated through intensive simulations and the analysis of a real data set from the Household Survey OHS99 conducted by Statistics South Africa.</p>

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Likelihood-based inference for interval censored regression models under heavy-tailed distributions

  • 期刊论文

  • 发表日期：

    2025年7月7日

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  • Yessenia A. Gil,
  • Aldo M. Garay,
  • Victor H. Lachos

摘要

Scale mixtures of skew-normal distributions form a class of asymmetric thick-tailed distributions that include skew-normal, skew-t, skew-contaminated normal, and the entire family of scale mixtures of normal distributions as special cases. This paper proposes an interval-censored linear regression model based on the class of scale mixtures of skew-normal distributions, providing an appealing, robust alternative to the usual Gaussian assumption in censored regression models. A novel Expectation/Conditional Maximization Either algorithm is proposed for maximum likelihood estimation, with analytical expressions at the E-step, as opposed to Monte Carlo simulations. These expressions rely on formulas for the mean and variance of truncated scale mixtures of skew-normal distributions that can be computed using the MomTrunc R package. The proposed methodology is illustrated through intensive simulations and the analysis of a real data set from the Household Survey OHS99 conducted by Statistics South Africa.