Regularly varying stochastic processes model extreme dependence between process values at different locations and/or time points. For such stationary processes we propose a two-step parameter estimation of the extremogram, when some part of the domain of interest is fixed and another increasing. We provide conditions for consistency and asymptotic normality of the empirical extremogram centred by a pre-asymptotic version for such observation schemes. For max-stable processes with Fréchet margins we provide conditions, such that the empirical extremogram (or a bias-corrected version) centred by its true version is asymptotically normal. In a second step, for a parametric extremogram model, we fit the parameters by generalised least squares estimation and prove consistency and asymptotic normality of the estimates. We propose subsampling procedures to obtain asymptotically correct confidence intervals. Finally, we apply our results to a variety of Brown-Resnick processes. A simulation study shows that the procedure works well also for moderate sample sizes.

中文翻译：

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基于灵活观测方案的规则变化时空过程的广义最小二乘估计

规则变化的随机过程对不同位置和/或时间点的过程值之间的极端依赖性进行建模。对于这样的平稳过程，当感兴趣区域的某个部分是固定的而另一部分是递增的时，我们建议对极值图进行两步参数估计。我们提供了以此类观察方案的渐近前版本为中心的经验极值图的一致性和渐近正态性的条件。对于具有Fréchet余量的最大稳定过程，我们提供了条件，使得以其真实形式为中心的经验极值图（或经偏差校正的版本）渐近是正常的。第二步，对于参数极值图模型，我们通过广义最小二乘估计拟合参数，并证明估计的一致性和渐近正态性。我们提出了二次抽样程序以获得渐近正确的置信区间。最后，我们将结果应用于各种Brown-Resnick过程。仿真研究表明，该程序对于中等样本量也适用。