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<p>This study develops a model that accounts for spatial and temporal heterogeneity in skewness and kurtosis to quantify uncertainty in spatio-temporal data. The proposed regression model, based on an extended flexible subclass of the closed skew-normal distribution (EFS-CSN), accommodates heterogeneous higher-order moments while preserving the mean and variance. This property ensures the interpretability of the regression coefficients and other parameters, as in conventional normal regression models. We also develop a fast Bayesian sampling procedure by exploiting conjugacy via data augmentation techniques. The estimation accuracy and predictive performance of the proposed EFS-CSN model are evaluated through Monte Carlo experiments. Lastly, the model is used to analyze state-level production functions in the United States.</p>

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Spatio-temporal heterogeneous skew-normal model with mean-variance preservation

  • 期刊论文

  • 发表日期：

    2026年7月7日

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  • Hajime Kuno,
  • Daisuke Murakami

摘要

This study develops a model that accounts for spatial and temporal heterogeneity in skewness and kurtosis to quantify uncertainty in spatio-temporal data. The proposed regression model, based on an extended flexible subclass of the closed skew-normal distribution (EFS-CSN), accommodates heterogeneous higher-order moments while preserving the mean and variance. This property ensures the interpretability of the regression coefficients and other parameters, as in conventional normal regression models. We also develop a fast Bayesian sampling procedure by exploiting conjugacy via data augmentation techniques. The estimation accuracy and predictive performance of the proposed EFS-CSN model are evaluated through Monte Carlo experiments. Lastly, the model is used to analyze state-level production functions in the United States.