Related papers: New type of extreme value statistics

Modeling distributions of covariates, or density estimation, is a core challenge in unsupervised learning. However, the majority of work only considers the joint distribution, which has limited utility in practical situations. A more…

In this paper we perform an analytical and numerical study of Extreme Value distributions in discrete dynamical systems that have a singular measure. Using the block maxima approach described in Faranda et al. [2011] we show that,…

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…

Motivated by observations that suggest the presence of extremely massive clusters at uncomfortably high redshifts for the standard cosmological model to explain, we develop a theoretical framework for the study of the most massive haloes,…

We establish a general framework to explore parametric statistics of individual energy levels in disordered and chaotic quantum systems of unitary symmetry. The method is applied to the calculation of the universal intra-level parametric…

These notes are based on lectures delivered by G. Schehr at the XVIth School on Fundamental Problems in Statistical Physics (FPSP), held in Oropa (Italy) from 30 June to 11 July 2025. After a brief introduction to extreme value statistics…

This work employs variational techniques to revisit and expand the construction and analysis of extreme value processes. These techniques permit a novel study of spatial statistics of the location of minimizing events. We develop integral…

We consider heavy-tailed distributions and compare the well-known estimators of the tail index, based on extreme value theory with a comparatively recent estimator based on a different idea.

Extremal quantile regression, i.e. quantile regression applied to the tails of the conditional distribution, counts with an increasing number of economic and financial applications such as value-at-risk, production frontiers, determinants…

Motivated by the psychological literature on the "peak-end rule" for remembered experience, we perform an analysis within a random walk framework of a discrete choice model where agents' future choices depend on the peak memory of their…

As an alternative to the well-known methods of "chaining" and "bracketing" that have been developed in the study of random fields, a new method, which is based on a {\em stochastic maximal inequality} derived by using the formula for…

Risk-sensitive reinforcement learning (RL) has garnered significant attention in recent years due to the growing interest in deploying RL agents in real-world scenarios. A critical aspect of risk awareness involves modeling highly rare risk…

We prove a new extremal inequality, motivated by the vector Gaussian broadcast channel and the distributed source coding with a single quadratic distortion constraint problems. As a corollary, this inequality yields a generalization of the…

Most of the existing classification methods are aimed at minimization of empirical risk (through some simple point-based error measured with loss function) with added regularization. We propose to approach this problem in a more information…

In this paper, we derive cumulant bounds for subgraph counts and power-weighted edge length in a class of spatial random networks known as weighted random connection models. This involves dealing with long-range spatial correlations induced…

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…

Standard maximum likelihood estimation cannot be applied to discrete energy-based models in the general case because the computation of exact model probabilities is intractable. Recent research has seen the proposal of several new…

Extreme events such as natural and economic disasters leave lasting impacts on society and motivate the analysis of extremes from data. While classical statistical tools based on Gaussian distributions focus on average behaviour and can…

Extreme value theory (EVT) is a statistical tool for analysis of extreme events. It has a strong theoretical background, however, we need to choose hyper-parameters to apply EVT. In recent studies of machine learning, techniques of choosing…

We address the question of condensation and extremes for three classes of intimately related stochastic processes: (a) random allocation models and zero-range processes, (b) tied-down renewal processes, (c) free renewal processes. While for…