Related papers: Frontier estimation and extreme value theory

In multivariate extreme value theory (MEVT), the focus is on analysis outside of the observable sampling zone, which implies that the region of interest is associated to high risk levels. This work provides tools to include directional…

This is a tutorial on some basic non-asymptotic methods and concepts in random matrix theory. The reader will learn several tools for the analysis of the extreme singular values of random matrices with independent rows or columns. Many of…

The method is proposed for the study of many-point boundary value problems for systems of nonlinear ODE, by reducing them to special equivalent integral equations, and allows us [in contrast with the known method [1]] to consider boundary…

An overview of existing nonparametric tests of extreme-value dependence is presented. Given an i.i.d.\ sample of random vectors from a continuous distribution, such tests aim at assessing whether the underlying unknown copula is of the {\em…

The classical multivariate extreme-value theory concerns the modeling of extremes in a multivariate random sample, suggesting the use of max-stable distributions. In this work, the classical theory is extended to the case where aggregated…

Statistical extreme value theory is concerned with the use of asymptotically motivated models to describe the extreme values of a process. A number of commonly used models are valid for observed data that exceed some high threshold.…

In this work, we deal with extreme value theory in the context of continued fractions using techniques from probability theory, ergodic theory and real analysis. We give an upper bound for the rate of convergence in the Doeblin-Iosifescu…

Convergence rate estimates in limit theorems for sums of independent random variables are considered.

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…

In risk management, often the probability must be estimated that a random vector falls into an extreme failure set. In the framework of bivariate extreme value theory, we construct an estimator for such failure probabilities and analyze its…

Extreme value theory provides rigorous theory and statistical tools for extrapolation in machine learning, particularly in settings where traditional methods struggle due to data scarcity in the tails. A broad range of tasks benefit from…

In this paper I develop a breakdown frontier approach to assess the sensitivity of Local Average Treatment Effects (LATE) estimates to violations of monotonicity and independence of the instrument. I parametrize violations of independence…

In this article we revisit the problem of numerical integration for monotone bounded functions, with a focus on the class of nonsequential Monte Carlo methods. We first provide new a lower bound on the maximal $L^p$ error of nonsequential…

This paper is concerned with estimating the intersection point of two densities, given a sample of both of the densities. This problem arises in classification theory. The main results provide lower bounds for the probability of the…

We discuss the use of likelihood asymptotics for inference on risk measures in univariate extreme value problems, focusing on estimation of high quantiles and similar summaries of risk for uncertainty quantification. We study whether…

The estimation of the covariance structure from a discretely observed multivariate Gaussian process under asynchronicity and noise is analysed under high-frequency asymptotics. Asymptotic lower and upper bounds are established for a general…

In this paper, we discuss the application of extreme value theory in the context of stationary $\beta$-mixing sequences that belong to the Fr\'echet domain of attraction. In particular, we propose a methodology to construct bias-corrected…

In this paper we focus on the study of the monotonicity properties of the residual and the past extropy as well as on some characterization problems. We then apply the derived results to analyze further stochastic aspects of order…

Due to the complexity of order statistics, the finite sample behaviour of robust statistics is generally not analytically solvable. While the Monte Carlo method can provide approximate solutions, its convergence rate is typically very slow,…

Data-driven anomaly detection methods typically build a model for the normal behavior of the target system, and score each data instance with respect to this model. A threshold is invariably needed to identify data instances with high (or…