基于柔性观测方案的规则变化时空过程的广义最小二乘估计
Generalised least squares estimation of regularly varying space-time processes based on flexible observation schemes
摘要：
规则变化的随机过程对不同位置和/或时间点处的过程值之间的极端依赖性进行建模。对于这样的过程，我们提出了一个两步参数估计的极值，当感兴趣的域的一部分是固定的，另一个增加。我们提供了条件的一致性和渐近正态性的经验极值中心的前渐近版本，这样的观察计划。对于具有Fr{é}chet边界的最大稳定过程，我们给出了条件，使得以其真实版本为中心的经验极值图（或偏差校正版本）渐近正态。第二步，对于参数极值模型，我们用广义最小二乘估计拟合参数，并证明了估计的相合性和渐近正态性。我们提出子抽样程序，以获得渐近正确的置信区间。最后，我们将我们的结果应用到各种Brown-Resnick过程。模拟研究表明，该程序也适用于中等样本量。
英文摘要：
Regularly varying stochastic processes model extreme dependence between process values at different locations and/or time points. For such 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 Fr{é}chet 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
