🤖 AI Summary
Existing spatial data models struggle to simultaneously capture complex extremal features such as tail dependence, asymptotic independence, and tail asymmetry. This work proposes a novel approach by introducing multivariate Pareto mixture distributions into a spatial copula framework, yielding a flexible model capable of jointly modeling both bulk and tail behaviors. The resulting formulation provides a unified treatment of the three aforementioned extremal dependence structures while preserving permutation asymmetry. Based on copula theory and maximum likelihood estimation, the method is validated through finite-sample simulations that demonstrate its computational feasibility and favorable parameter estimation performance. Empirical analysis of temperature data successfully reveals intricate tail structures, underscoring the model’s theoretical rigor and practical utility.
📝 Abstract
This paper introduces a class of copula models for spatial data, based on multivariate Pareto-mixture distributions. We explore the tail properties of these models, demonstrating their ability to capture both tail dependence and asymptotic independence, as well as the tail asymmetry frequently observed in real-world data. The proposed models also offer flexibility in accounting for permutation asymmetry and can effectively represent both the bulk and extreme tails of the distribution. We consider special cases of these models with computationally tractable likelihoods and present an extensive simulation study to assess the finite-sample performance of the maximum likelihood estimators. Finally, we apply our models to analyze a temperature dataset, showcasing their practical utility.