Related papers: Discrete Extremes
We investigate the statistical properties of the extreme events of the solar cycle as measured by the sunspot number. The recent advances in the methodology of the theory of extreme values is applied to the maximal extremes of the time…
We study the problem of selecting features associated with extreme values in high dimensional linear regression. Normally, in linear modeling problems, the presence of abnormal extreme values or outliers is considered an anomaly which…
The masses of data now available have opened up the prospect of discovering weak signals using machine-learning algorithms, with a view to predictive or interpretation tasks. As this survey of recent results attempts to show, bringing…
This paper introduces a method for spatial interpolation of extreme values, and in particular targets the case in which conventional data, resulting from a measurement for example, are available at only a few locations. To overcome this the…
Causal effect estimation seeks to determine the impact of an intervention from observational data. However, the existing causal inference literature primarily addresses treatment effects on frequently occurring events. But what if we are…
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…
Extreme quantile regression provides estimates of conditional quantiles outside the range of the data. Classical quantile regression performs poorly in such cases since data in the tail region are too scarce. Extreme value theory is used…
The generalized Pareto distribution (GPD) is a fundamental model for analyzing the tail behavior of a distribution. In particular, the shape parameter of the GPD characterizes the extremal properties of the distribution. As described in…
Regular vine sequences permit the organisation of variables in a random vector along a sequence of trees. Regular vine models have become greatly popular in dependence modelling as a way to combine arbitrary bivariate copulas into…
We introduce methods to bound the mean of a discrete distribution (or finite population) based on sample data, for random variables with a known set of possible values. In particular, the methods can be applied to categorical data with…
In extreme values theory, for a sufficiently large block size, the maxima distribution is approximated by the generalized extreme value (GEV) distribution. The GEV distribution is a family of continuous probability distributions, which has…
In a wide variety of situations, anomalies in the behaviour of a complex system, whose health is monitored through the observation of a random vector X = (X1,. .. , X d) valued in R d , correspond to the simultaneous occurrence of extreme…
For measuring tail risk with scarce extreme events, extreme value analysis is often invoked as the statistical tool to extrapolate to the tail of a distribution. The presence of large datasets benefits tail risk analysis by providing more…
In many applied fields, the prediction of more severe events than those already recorded is crucial for safeguarding against potential future calamities. What-if analyses, which evaluate hypothetical scenarios up to the worst-case event,…
The tail of a bivariate distribution function in the domain of attraction of a bivariate extreme-value distribution may be approximated by the one of its extreme-value attractor. The extreme-value attractor has margins that belong to a…
Although the fundamental probabilistic theory of extremes has been well developed, there are many practical considerations that must be addressed in application. The contribution of this thesis is four-fold. The first concerns the choice of…
The weighted average is by far the most popular approach to combining multiple forecasts of some future outcome. This paper shows that both for probability or real-valued forecasts, a non-trivial weighted average of different forecasts is…
Multivariate peaks over thresholds modeling based on generalized Pareto distributions has up to now only been used in few and mostly 2-dimensional situations. This paper contributes theoretical understanding, physically based models,…
Extreme value theory is concerned with probabilistic and statistical questions related to very high or very low values in sequences of random variables and in stochastic processes. The subject has a rich mathematical theory and also a long…
The Zipf distribution also known as scale-free distribution or discrete Pareto distribution, is the particular case of Power Law distribution with support the strictly positive integers. It is a one-parameter distribution with a linear…