Related papers: Strong Convergence of Peaks Over a Threshold
We suggest approximating the distribution of the sum of independent and identically distributed random variables with a Pareto-like tail by combining extreme value approximations for the largest summands with a normal approximation for the…
We study the extremes for a class of a symmetric stable random fields with long range dependence. We prove functional extremal theorems both in the space of sup measures and in the space of cadlag functions of several variables. The limits…
A coupling method is developed for univariate extreme value theory , providing an alternative to the use of the tail empirical/quantile processes. Emphasizing the Peak-over-Threshold approach that approximates the distribution above high…
We study distributional robustness in the context of Extreme Value Theory (EVT). We provide a data-driven method for estimating extreme quantiles in a manner that is robust against incorrect model assumptions underlying the application of…
We consider the extreme value statistics of $N$ independent and identically distributed random variables, which is a classic problem in probability theory. When $N\to\infty$, fluctuations around the maximum of the variables are described by…
We revisit multivariate extreme value theory modeling by emphasizing multivariate regular variations and the multivariate Breiman Lemma. This allows us to recover in a simple framework the most popular multivariate extreme value…
Testing whether two multivariate samples exhibit the same extremal behavior is an important problem in various fields including environmental and climate sciences. While several ad-hoc approaches exist in the literature, they often lack…
When modeling a vector of risk variables, extreme scenarios are often of special interest. The peaks-over-thresholds method hinges on the notion that, asymptotically, the excesses over a vector of high thresholds follow a multivariate…
This brief paper summarize the chances offered by the Peak-Over-Threshold method, related with analysis of extremes. Identification of appropriate Value at Risk can be solved by fitting data with a Generalized Pareto Distribution. Also an…
We study extremal statistics and return intervals in stationary long-range correlated sequences for which the underlying probability density function is bounded and uniform. The extremal statistics we consider e.g., maximum relative to…
In this article we show the relationship between the Pareto distribution and the gamma distribution. This shows that the second one, appropriately extended, explains some anomalies that arise in the practical use of extreme value theory.…
Neural networks are able to approximate any continuous function on a compact set. However, it is not obvious how to quantify the error of the neural network, i.e., the remaining bias between the function and the neural network. Here, we…
In many applied fields it is desired to make predictions with the aim of assessing the plausibility of more severe events than those already recorded to safeguard against calamities that have not yet occurred. This problem can be analysed…
Suppose Xt is either a regular exponential type Levy process or a Levy process with a bounded variation jumps measure. The distribution of the extrema of Xt play a crucial role in many financial and actuarial problems. This article employs…
Extreme value distributions are routinely employed to assess risks connected to extreme events in a large number of applications. They typically are two- or three- parameter distributions: the inference can be unstable, which is…
Analysis of the rare and extreme values through statistical modeling is an important issue in economical crises, climate forecasting, and risk management of financial portfolios. Extreme value theory provides the probability models needed…
For extreme value estimation we propose to use a model with a Dirichlet process mixture of gamma densities in the center and generalized Pareto densities for the tails. Due to the randomness in the center and a heavy tailed density in the…
Our contribution is to widen the scope of extreme value analysis applied to discrete-valued data. Extreme values of a random variable $X$ are commonly modeled using the generalized Pareto distribution, a method that often gives good results…
The families of $f$-divergences (e.g. the Kullback-Leibler divergence) and Integral Probability Metrics (e.g. total variation distance or maximum mean discrepancies) are widely used to quantify the similarity between probability…
We use the fitted Pareto law to construct an accompanying approximation of the excess distribution function. A selection rule of the location of the excess distribution function is proposed based on a stagewise lack-of-fit testing…