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

Author

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  • Yessenia A. Gil

    (Federal University of Pernambuco)

  • Aldo M. Garay

    (Federal University of Pernambuco)

  • Victor H. Lachos

    (University of Connecticut)

Abstract

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.

Suggested Citation

  • Yessenia A. Gil & Aldo M. Garay & Victor H. Lachos, 2025. "Likelihood-based inference for interval censored regression models under heavy-tailed distributions," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 34(3), pages 519-544, July.
    • Handle: RePEc:spr:stmapp:v:34:y:2025:i:3:d:10.1007_s10260-025-00797-x
    DOI: 10.1007/s10260-025-00797-x
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