标题： 最大复合似然估计量在固定域上对极大稳定布朗-雷斯尼克随机场的渐近性质 显示英文标题

标题： Asymptotic properties of maximum composite likelihood estimators for max-stable Brown-Resnick random fields over a fixed-domain

摘要： 最大稳定随机场的似然推断通常是不可能的，因为它们的有限维概率密度函数是未知的或无法高效计算。 利用较低维边缘似然（通常是距离不太远的站点对或三元组）的加权复合似然方法更为常用。 在本文中，我们考虑与各向同性分数布朗场相关的空间最大稳定布朗-雷斯尼克随机场族。 我们假设站点仅由限制在$\mathbf{C}=(-1/2,1/2]^{2}$上的齐次泊松点过程的一个实现给出，并且随机场在这些站点上被观测到。 随着强度的增加，我们使用不同的加权策略研究了分数布朗场尺度参数和赫斯特参数的复合似然估计量的渐近性质：我们排除那些不是Delaunay三角剖分边的对，或者不是三角形顶点的三元组。 显示英文摘要

摘要： Likelihood inference for max-stable random fields is in general impossible because their finite-dimensional 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.