Related papers: On Regression in Extreme Regions
The study of loss function distributions is critical to characterize a model's behaviour on a given machine learning problem. For example, while the quality of a model is commonly determined by the average loss assessed on a testing set,…
To provide a comprehensive summary of the tail distribution, the expected shortfall is defined as the average over the tail above (or below) a certain quantile of the distribution. The expected shortfall regression captures the…
The most popular approach in extreme value statistics is the modelling of threshold exceedances using the asymptotically motivated generalised Pareto distribution. This approach involves the selection of a high threshold above which the…
We study the problem of linear regression where both covariates and responses are potentially (i) heavy-tailed and (ii) adversarially contaminated. Several computationally efficient estimators have been proposed for the simpler setting…
We introduce a new regression method that relates the mean of an outcome variable to covariates, under the "adverse condition" that a distress variable falls in its tail. This allows to tailor classical mean regressions to adverse…
We study the asymptotic behaviour of widely used tests for evaluating and comparing predictive accuracy when forecast errors exhibit heavy tails. In particular, when loss differentials have infinite variance, the Diebold-Mariano test…
Covariate shift is a common transfer learning scenario where the marginal distributions of input variables vary between source and target data while the conditional distribution of the output variable remains consistent. The existing…
In this paper, we propose a reduced-bias estimator of the EVI for Pareto-type tails (heavy-tailed) distributions. This is derived using the weighted least squares method. It is shown that the estimator is unbiased, consistent and…
We propose a semiparametric method for fitting the tail of a heavy-tailed population given a relatively small sample from that population and a larger sample from a related background population. We model the tail of the small sample as an…
By introducing a weight function into the density power divergence, we develop a new class of robust and smooth estimators for the tail index of Pareto-type distributions, offering improved efficiency in the presence of outliers. These…
The notion of expectiles, originally introduced in the context of testing for homoscedasticity and conditional symmetry of the error distribution in linear regression, induces a law-invariant, coherent and elicitable risk measure that has…
We investigate how to learn treatment effects away from the cutoff in multiple-cutoff regression discontinuity designs. Using a microeconomic model, we demonstrate that the parallel-trend type assumption proposed in the literature is…
This paper considers the specification of covariance structures with tail estimates. We focus on two aspects: (i) the estimation of the VaR-CoVaR risk matrix in the case of larger number of time series observations than assets in a…
We study the empirical version of halfspace depths with the objective of establishing a connection between the rates of convergence and the tail behaviour of the corresponding underlying distributions. The intricate interplay between the…
We provide a new extension of Breiman's Theorem on computing tail probabilities of a product of random variables to a multivariate setting. In particular, we give a complete characterization of regular variation on cones in $[0,\infty)^d$…
We conduct a non asymptotic study of the Cross Validation (CV) estimate of the generalization risk for learning algorithms dedicated to extreme regions of the covariates space. In this Extreme Value Analysis context, the risk function…
This paper proposes a specification test for the conventional distributional assumptions of error terms in binary choice models, focusing on its tail properties. Based on extreme value theory, we first establish that the tail index of the…
Diversity schemes play a vital role in improving the performance of ultra-reliable communication systems by transmitting over two or more communication channels to combat fading and co-channel interference. Determining an appropriate…
Extremes play a special role in Anomaly Detection. Beyond inference and simulation purposes, probabilistic tools borrowed from Extreme Value Theory (EVT), such as the angular measure, can also be used to design novel statistical learning…
Linear regression is ubiquitous in statistical analysis. It is well understood that conflicting sources of information may contaminate the inference when the classical normality of errors is assumed. The contamination caused by the light…