Cross-covariance functions for multivariate random fields based on latent dimensions

• 成果类型: Article
• 署名作者: Apanasovich, Tatiyana V.; Genton, Marc G.
• 署名单位: Thomas Jefferson University; Texas A&M University System; Texas A&M University College Station
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asp078
• 发表日期: 2010
• 页码: 1530
• 关键词: model

摘要

The problem of constructing valid parametric cross-covariance functions is challenging. We propose a simple methodology, based on latent dimensions and existing covariance models for univariate random fields, to develop flexible, interpretable and computationally feasible classes of cross-covariance functions in closed form. We focus on spatio-temporal cross-covariance functions that can be nonseparable, asymmetric and can have different covariance structures, for instance different smoothness parameters, in each component. We discuss estimation of these models and perform a small simulation study to demonstrate our approach. We illustrate our methodology on a trivariate spatio-temporal pollution dataset from California and demonstrate that our cross-covariance performs better than other competing models.