Related papers: Statistical Prediction of Peaks Over a Threshold
Applying standard statistical methods after model selection may yield inefficient estimators and hypothesis tests that fail to achieve nominal type-I error rates. The main issue is the fact that the post-selection distribution of the data…
The predictability of errors in deterministic temperature forecasts is investigated. More precisely, the aim is to issue warnings whenever the differences between forecast and verification exceed a given threshold. The warnings are…
Threshold selection is a fundamental problem in any threshold-based extreme value analysis. While models are asymptotically motivated, selecting an appropriate threshold for finite samples is difficult and highly subjective through standard…
One of the goals of climate science is to characterize the statistics of extreme and potentially dangerous events in the present and future climate. Extreme events like heat waves, droughts, or floods due to persisting rains are…
Accurately quantifying tail risks-rare but high-impact events such as financial crashes or extreme weather-is a central challenge in risk management, with serially dependent data. We develop a Bayesian framework based on the Generalized…
A weighted Gaussian approximation to tail product-limit process for Pareto-like distributions of randomly right-truncated data is provided and a new consistent and asymptotically normal estimator of the extreme value index is derived. A…
We investigate the frequentist coverage of Bayesian credible sets in a nonparametric setting. We consider a scale of priors of varying regularity and choose the regularity by an empirical Bayes method. Next we consider a central set of…
\cite{HillMotegi2017} present a new general asymptotic theory for the maximum of a random array $\{\mathcal{X}_{n}(i)$ $:$ $1$ $\leq $ $i$ $\leq $ $\mathcal{L}\}_{n\geq 1}$, where each $\mathcal{X}_{n}(i)$ is assumed to converge in…
Accurate modeling is essential in integer-valued real phenomena, including the distribution of entire data, zero-inflated (ZI) data, and discrete exceedances. The Poisson and Negative Binomial distributions, along with their ZI variants,…
Multivariate extreme value statistical analysis is concerned with observations on several variables which are thought to possess some degree of tail-dependence. In areas such as the modeling of financial and insurance risks, or as the…
In a low-order model of the general circulation of the atmosphere we examine the predictability of threshold exceedance events of certain observables. The likelihood of such binary events -- the cornerstone also for the categoric (as…
Preferential sampling is a common feature in geostatistics and occurs when the locations to be sampled are chosen based on information about the phenomena under study. In this case, point pattern models are commonly used as the probability…
We present a quasi-conjugate Bayes approach for estimating Generalized Pareto Distribution (GPD) parameters, distribution tails and extreme quantiles within the Peaks-Over-Threshold framework. Damsleth conjugate Bayes structure on Gamma…
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…
A common approach to modelling extreme values is to consider the excesses above a high threshold as realisations of a non-homogeneous Poisson process. While this method offers the advantage of modelling using threshold-invariant extreme…
Parametric density estimation, for example as Gaussian distribution, is the base of the field of statistics. Machine learning requires inexpensive estimation of much more complex densities, and the basic approach is relatively costly…
The two statistical methods, namely the frequentist and the Bayesian methods, are both commonly used for probabilistic inference in many scientific situations. However, it is not straightforward to interpret the result of one approach in…
Outer measures can be used for statistical inference in place of probability measures to bring flexibility in terms of model specification. The corresponding statistical procedures such as Bayesian inference, estimators or hypothesis…
In extreme value analysis, tail behavior of a heavy-tailed data distribution is modeled by a Pareto-type distribution in which the so-called extreme value index (EVI) controls the tail behavior. For heavy-tailed data obtained from multiple…
Extreme value applications commonly employ regression techniques to capture cross-sectional heterogeneity or time-variation in the data. Estimation of the parameters of an extreme value regression model is notoriously challenging due to the…