相关论文: Extrapolation of max-stable random fields with Fr\…

In this paper, we discuss three extrapolation methods for alpha-stable random fields with 1<alpha<=2. We justify them, giving proofs of the existence and uniqueness of the solutions for each method and providing sufficient conditions for…

In this paper, we use the concept of excursion sets for the extrapolation of stationary random fields. Doing so, we define excursion sets for the field and its linear predictor, and then minimize the expected volume of the symmetric…

We consider the random field M(t)=\sup_{n\geq 1}\big\{-\log A_{n}+X_{n}(t)\big\}\,,\qquad t\in T\, for a set $T\subset \mathbb{R}^{m}$, where $(X_{n})$ is an iid sequence of centered Gaussian random fields on $T$ and $0<A_{1}<A_{2}<\cdots $…

We study the probability distribution of the maximum $M_S $ of a smooth stationary Gaussian field defined on a fractal subset $S$ of $\R^n$. Our main result is the equivalent of the asymptotic behavior of the tail of the distribution…

We use the concept of excursions for the prediction of random variables without any moment existence assumptions. To do so, an excursion metric on the space of random variables is defined which appears to be a kind of a weighted…

In practice, it is not possible to observe a whole max-stable random field. Therefore, a way how to reconstruct a max-stable random field in $C\left([0,1]^k\right)$ by interpolating its realizations at finitely many points is proposed. The…

In this paper, we show how the sampling properties of the Hurst exponent methods of estimation change with the presence of heavy tails. We run extensive Monte Carlo simulations to find out how rescaled range analysis (R/S), multifractal…

In this paper, a novel approach to the problem of estimating the heavy-tail exponent alpha>0 of a distribution is proposed. It is based on the fact that block-maxima of size m of the independent and identically distributed data scale at a…

We show how to perform full likelihood inference for max-stable multivariate distributions or processes based on a stochastic Expectation-Maximisation algorithm, which combines statistical and computational efficiency in high-dimensions.…

Max-stable random fields play a central role in modeling extreme value phenomena. We obtain an explicit formula for the conditional probability in general max-linear models, which include a large class of max-stable random fields. As a…

We introduce basic statistical methods for the extrapolation of stationary random fields. For square integrable fields, we set out basics of the kriging extrapolation techniques. For (non--Gaussian) stable fields, which are known to be…

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…

We develop goodness-of-fit tests for max-stable random fields, which are used to model heavy-tailed spatial data. The test statistics are constructed based on the Fourier transforms of the indicators of extreme values in the heavy-tailed…

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…

We offer in this paper the non-asymptotical bilateral sharp exponential estimates for tail of maximum distribution of {\it discontinuous} random fields. Our consideration based on the theory of Prokhorov-Skorokhod spaces of random fields…

Max-stable processes have proved to be useful for the statistical modelling of spatial extremes. Several representations of max-stable random fields have been proposed in the literature. For statistical inference it is often assumed that…

Let $\{X(t)= (X_1(t),X_2(t))^T,\ t \in \mathbb{R}^N\}$ be an $\mathbb{R}^2$-valued continuous locally stationary Gaussian random field with $\mathbb{E}[X(t)]=\mathbf{0}$. For any compact sets $A_1, A_2 \subset \mathbb{R}^N$, precise…

Stable distributions provide a flexible framework for modeling heavy-tailed and skewed data, with the stability index $\alpha$ quantifying tail heaviness. We propose a new semiparametric estimator for $\alpha$ that leverages the two-sum…

Heavy-tailed distributions are widely used in robust mixture modelling due to possessing thick tails. As a computationally tractable subclass of the stable distributions, sub-Gaussian $\alpha$-stable distribution received much interest in…

The class of $\alpha$-stable distributions with a wide range of applications in economics, telecommunications, biology, applied, and theoretical physics. This is due to the fact that it possesses both the skewness and heavy tails. Since…