论文标题
最大复合可能性估计器的最大稳定棕色呈随机场的固定域渐近性特性
Fixed-domain asymptotic properties of maximum composite likelihood estimators for max-stable Brown-Resnick random fields
论文作者
论文摘要
最大稳定随机场的可能性推断是不可能的，因为它们的有限二二个概率密度函数是未知的，或者无法有效地计算出来。使用较低维的边际似然的加权复合可能性方法（通常是对不太遥远的位点的成对或三元组）。在本文中，我们考虑了与各向同性分数布朗田的空间最大棕色呈棕色晶体随机场。我们假设该站点仅通过一个实现均匀的泊松点过程给出，仅限于$ \ MATHBF {C} =（ - 1/1/2,1/2]^{2} $给出，并且随着这些站点的观察到随机字段。随着这些强度的增加，我们会使用该尺度和尺度的范围范围的范围范围估算师的范围范围的范围差异。策略：我们排除了不是Delaunay三角剖分边缘的对，或者不是三角形顶点的三倍。
Likelihood inference for max-stable random fields is in general impossible because their finite-dimen\-sional probability density functions are unknown or cannot be computed efficiently. The weighted composite likelihood approach that utilizes lower dimensional marginal likelihoods (typically pairs or triples of sites that are not too distant) is rather favored. In this paper, we consider the family of spatial max-stable Brown-Resnick random fields associated with isotropic fractional Brownian fields. We assume that the sites are given by only one realization of a homogeneous Poisson point process restricted to $\mathbf{C}=(-1/2,1/2]^{2}$ and that the random field is observed at these sites. As the intensity increases, we study the asymptotic properties of the composite likelihood estimators of the scale and Hurst parameters of the fractional Brownian fields using different weighting strategies: we exclude either pairs that are not edges of the Delaunay triangulation or triples that are not vertices of triangles.
