Modeling heterogeneity in higher-order moments while preserving mean and variance: application to spatio-temporal modeling

TL;DR

This paper introduces a flexible statistical model that captures heterogeneity in higher-order moments like skewness and kurtosis while preserving mean and variance, with applications to spatial-temporal data and production functions.

Contribution

It presents a novel, interpretable model that handles heterogeneity in higher moments, is closed under linear transformations, and includes a Bayesian inference approach for efficient estimation.

Findings

Model effectively captures heterogeneity in higher moments.

Bayesian inference improves parameter estimation and prediction.

Application to U.S. state data shows superior fit.

Abstract

In this study, we propose a general model capable of addressing heterogeneity in higher-order moments while preserving mean and variance, including the t, Laplace, and skew-normal distributions as special cases. Our model flexibly accommodates variations in tail heaviness and asymmetry at each data point while maintaining interpretability similar to normal distribution models. Notably, it is closed under linear transformations and provides explicit analytical expressions for skewness and kurtosis. The proposed model is applied to spatial and temporal data analysis, demonstrating that its properties vary based on the chosen matrix decomposition approach. To facilitate efficient inference, we develop a Bayesian estimation method using data augmentation, which is particularly effective for temporal models. Simulation studies confirm that accounting for heterogeneity in higher-order moments enhances parameter estimation accuracy and predictive performance. To illustrate real-world applicability, we analyze production functions across U.S. states. The results indicate that our model effectively captures heterogeneity in higher-order moments, leading to superior model fit in empirical data analysis.