We consider a strictly stationary random field on the two-dimensional integer lattice with regularly varying marginal and finite-dimensional distributions. Exploiting the regular variation, we define the spatial extremogram which takes into account only the largest values in the random field. This extremogram is a spatial autocovariance function. We define the corresponding extremal spectral density and its estimator, the extremal periodogram. Based on the extremal periodogram, we consider the Whittle estimator for suitable classes of parametric random fields including the Brown-Resnick random field and regularly varying max-moving averages.
A note on estimation of $α$-stable CARMA processes sampled at low frequencies
本文研究了等距采样对称$α$稳定CARMA过程的估计.模拟研究表明，Whittle估计量和Garc 'ıa等人（2011）提出的估计量是稳定CARMA过程参数的一致估计量。对于具有有限二阶矩的CARMA过程，Whittle估计是相合的且渐近正态分布。因此，在轻尾设置的CARMA过程的Whittle估计的性质是类似的ARMA过程的Whittle估计。然而，在本文中，我们证明，在一般情况下，对称$α$稳定的CARMA过程在低频率采样的惠特尔估计是不一致的，并强调为什么模拟研究表明别的东西。因此，与轻尾设置相比，重尾ARMA过程的Whittle估计的性质不能转移到重尾CARMA过程。我们也阐述了Garc 'ıa et al.（2011）中提出的估计量面临同样的问题。然而，稳定CAR（1）过程的Whittle估计是一致的。
Statistical inference for heavy tailed series with extremal independence
本文考虑平稳时间序列$\{X_j, j \in Z\} whose finite dimensional distributions are regularly varying with extremal independence. We assume that for each $ h \geq 1 $, conditionally on $ X 0 $ to exceed a threshold tending to infinity, the conditional distribution of $ X h$适当归一化弱收敛到一个非退化分布.在本文中，我们考虑估计的正常化和极限分布。
On the parametric and semiparametric Fisher information matrix for non-zero mean stationary spherical invariant random processes
Samovar laboratory, Telecom SudParis, Institut Polytechnique de Paris（萨莫瓦尔实验室，电信巴黎理工学院，巴黎理工学院）；Taif University, College of Engineering, Dept. of Electrical Engineering（塔伊夫大学，工程学院，电气工程系）
Central limit theory for serial tail dependence estimators in heavy-tailed long memory linear time series
University of Stuttgart（斯图加特大学）；Stuttgart Center for Simulation Science (SC SimTech), University of Stuttgart（斯图加特大学斯图加特模拟科学中心）；Univ Angers, CNRS, LAREMA, SFR MATHSTIC（昂热大学、法国国家科学研究中心、LAREMA、MATHSTIC研究联盟）
