论文标题
融合凯奇和马特恩协方差函数的融合论点
Convergence Arguments to Bridge Cauchy and Matérn Covariance Functions
论文作者
论文摘要
Matérn和广义的协方差函数家族在空间统计以及大量统计应用中发挥着重要作用。 Matérn家族对于相关的高斯随机场的指数均方根可不同。 Cauchy家族是对不相似的高斯随机场的分形维度和赫斯特效应的脱钩者。 我们的努力是为了证明，作为对广义凯奇家族的重新聚集的量表依赖性的协方差函数家族，将其收敛于Matérn家族的特定情况，从而提供了带有光量子和协方差模型之间的协调模型之间有些令人惊讶的桥梁，从而允许长期记忆效应。
The Matérn and the Generalized Cauchy families of covariance functions have a prominent role in spatial statistics as well as in a wealth of statistical applications. The Matérn family is crucial to index mean-square differentiability of the associated Gaussian random field; the Cauchy family is a decoupler of the fractal dimension and Hurst effect for Gaussian random fields that are not self-similar. Our effort is devoted to prove that a scale-dependent family of covariance functions, obtained as a reparameterization of the Generalized Cauchy family, converges to a particular case of the Matérn family, providing a somewhat surprising bridge between covariance models with light tails and covariance models that allow for long memory effect.
