Related papers: On the Tail Behaviour of Aggregated Random Variabl…
Anomaly detection methods are widely used but often rely on ad hoc rules or strong assumptions, and they often focus on tail events, missing ``inlier'' anomalies that occur in low-density gaps between modes. We propose a unified framework…
A notion of tail dependence based on operator regular variation is introduced for copulas, and the standard tail dependence used in the copula literature is included as a special case. The non-standard tail dependence with marginal power…
We demonstrate both analytically and numerically that the existing methods for measuring tail dependence in copulas may sometimes underestimate the extent of extreme co-movements of dependent risks and, therefore, may not always comply with…
Statistical modeling of high dimensional extremes remains challenging and has generally been limited to moderate dimensions. Understanding structural relationships among variables at their extreme levels is crucial both for constructing…
We consider the clustering of extremes for stationary regularly varying random fields over arbitrary growing index sets. We study sufficient assumptions on the index set such that the limit of the point random fields of the exceedances…
Extreme value theory offers a statistical framework for quantifying the risk of rare events, with the generalized Pareto (GP) distribution providing the canonical limit model for univariate threshold exceedances. In many applications,…
We study tail behaviour of the distribution of the area under the positive excursion of a random walk which has negative drift and heavy-tailed increments. We determine the asymptotics for tail probabilities for the area.
We study large deviation probabilities for a sum of dependent random variables from a heavy-tailed factor model, assuming that the components are regularly varying. We identify conditions where both the factor and the idiosyncratic terms…
Given two multivariate copulas with corresponding tail dependence functions, we investigate the relation between a natural tail dependence ordering $\leq_{tdo}$ and the order $\leq_{loc}$ of local stochastic dominance. We show that,…
We consider a multivariate heavy-tailed stochastic volatility model and analyze the large-sample behavior of its sample covariance matrix. We study the limiting behavior of its entries in the infinite-variance case and derive results for…
We introduce a new class of heavy-tailed distributions for which any weighted average of independent and identically distributed random variables is larger than one such random variable in (usual) stochastic order. We show that many…
The most popular approach in extreme value statistics is the modelling of threshold exceedances using the asymptotically motivated generalised Pareto distribution. This approach involves the selection of a high threshold above which the…
We consider the empirical versions of geometric quantile and halfspace depth, and study their extremal behaviour as a function of the sample size. The objective of this study is to establish connection between the rates of convergence and…
We study the upper tail of the number of arithmetic progressions of a given length in a random subset of {1,...,n}, establishing exponential bounds which are best possible up to constant factors in the exponent. The proof also extends to…
We consider two independent random variables with the given tail asymptotic (e.g. power or exponential). We find tail asymptotic for their sum and product. This is done by some cumbersome but purely technical computations and requires the…
We propose a novel extremal dependence measure called the partial tail-correlation coefficient (PTCC), in analogy to the partial correlation coefficient in classical multivariate analysis. The construction of our new coefficient is based on…
The upper tail problem for the largest eigenvalue of the Erd\H{o}s--R\'enyi random graph $\mathcal{G}_{n,p}$ is to estimate the probability that the largest eigenvalue of the adjacency matrix of $\mathcal{G}_{n,p}$ exceeds its typical value…
Inference over tails is usually performed by fitting an appropriate limiting distribution over observations that exceed a fixed threshold. However, the choice of such threshold is critical and can affect the inferential results. Extreme…
The asymptotic results that underlie applications of extreme random fields often assume that the variables are located on a regular discrete grid, identified with $\mathbb{Z}^2$, and that they satisfy stationarity and isotropy conditions.…
In this thesis, the tail properties of multivariate Archimedean copulas are investigated using known representation theorems involving L1-norm symmetric distributions and the Williamson d-transform. Several new results on the asymptotic…