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Related papers: Tail calibration of probabilistic forecasts

200 papers

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.

Probability · Mathematics 2016-08-14 Vygantas Paulauskas , Marijus Vaičiulis

A novel forecast combination and weighted quantile based tail-risk forecasting framework is proposed, aiming to reduce the impact of modelling uncertainty in tail-risk forecasting. The proposed approach is based on a two-step estimation…

Risk Management · Quantitative Finance 2021-07-20 Giuseppe Storti , Chao Wang

Predicting not only the target but also an accurate measure of uncertainty is important for many machine learning applications and in particular safety-critical ones. In this work we study the calibration of uncertainty prediction for…

Machine Learning · Computer Science 2020-02-04 Dan Levi , Liran Gispan , Niv Giladi , Ethan Fetaya

Risk measures, which typically evaluate the impact of extreme losses, are highly sensitive to misspecification in the tails. This paper studies a robust optimization approach to combat tail uncertainty by proposing a unifying framework to…

Optimization and Control · Mathematics 2024-12-09 Guanyu Jin , Roger J. A. Laeven , Dick den Hertog , Aharon Ben-Tal

Extreme events and the heavy tail distributions driven by them are ubiquitous in various scientific, engineering and financial research. They are typically associated with stochastic instability caused by hidden unresolved processes.…

Probability · Mathematics 2019-05-22 Andrew J. Majda , Xin T. Tong

Calibration is a classical notion from the forecasting literature which aims to address the question: how should predicted probabilities be interpreted? In a world where we only get to observe (discrete) outcomes, how should we evaluate a…

Machine Learning · Computer Science 2025-09-03 Parikshit Gopalan , Lunjia Hu

The key to successful statistical analysis of bivariate extreme events lies in flexible modelling of the tail dependence relationship between the two variables. In the extreme value theory literature, various techniques are available to…

Methodology · Statistics 2025-05-05 Emma S. Simpson , Jonathan A. Tawn

Probability forecasts are intended to account for the uncertainties inherent in forecasting. It is suggested that from an end-user's point of view probability is not necessarily sufficient to reflect uncertainties that are not simply the…

Statistics Theory · Mathematics 2015-01-22 Kevin Judd

Probabilistic forecasts are becoming more and more available. How should they be used and communicated? What are the obstacles to their use in practice? I review experience with five problems where probabilistic forecasting played an…

Applications · Statistics 2014-08-22 Adrian E. Raftery

The relationship between a response variable and its covariates can vary significantly, especially in scenarios where covariates take on extremely high or low values. This paper introduces a max-linear tail regression model specifically…

Methodology · Statistics 2025-02-24 Liujun Chen , Deyuan Li , Zhengjun Zhang

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 $[0,\infty)^d$…

Probability · Mathematics 2020-06-09 Bikramjit Das , Vicky Fasen-Hartmann , Claudia Klüppelberg

We extend known saddlepoint tail probability approximations to multivariate cases, including multivariate conditional cases. Our approximation applies to both continuous and lattice variables, and requires the existence of a cumulant…

Statistics Theory · Mathematics 2010-11-29 John Kolassa , Jixin Li

There is given a method for estimation of a probability distribution tail in terms of characteristic function. Key words: characteristic function; tail of a distribution.

Probability · Mathematics 2016-07-12 Lev B. Klebanov , Andrea Karlova

Measures of tail dependence between random variables aim to numerically quantify the degree of association between their extreme realizations. Existing tail dependence coefficients (TDCs) are based on an asymptotic analysis of relevant…

Applications · Statistics 2021-06-11 Davide Lauria , Svetlozar T. Rachev , A. Alexandre Trindade

The task of estimation of the tails of probability distributions having small samples seems to be still opened and almost unsolvable. The paper tries to make a step in filling this gap. In 2017 Jordanova et al. introduce six new…

Statistics Theory · Mathematics 2018-11-14 Pavlina Jordanova , Monika Peteva

Inference over tails is usually performed by fitting an appropriate limiting distribution over observations that exceed a fixed threshold. However, the choice of such threshold is critical and can affect the inferential results. Extreme…

Statistical Finance · Quantitative Finance 2019-02-26 Chiara Lattanzi , Manuele Leonelli

We propose notions of calibration for probabilistic forecasts of general multivariate quantities. Probabilistic copula calibration is a natural analogue of probabilistic calibration in the univariate setting. It can be assessed empirically…

Methodology · Statistics 2013-07-30 Johanna F. Ziegel , Tilmann Gneiting

The authors announce a general tail estimate, called a decoupling inequality, for a symmetrized sum of non-linear $k$-correlations of $n>k$ independent random variables.

Functional Analysis · Mathematics 2016-09-06 Victor H. de la Peña , Stephen J. Montgomery-Smith

This thesis evaluates most of the extreme mixture models and methods that have appended in the literature and implements them in the context of finance and insurance. The paper also reviews and studies extreme value theory, time series,…

General Economics · Economics 2024-07-09 Yujuan Qiu

Chebyshev's inequality provides an upper bound on the tail probability of a random variable based on its mean and variance. While tight, the inequality has been criticized for only being attained by pathological distributions that abuse the…

Optimization and Control · Mathematics 2020-10-16 Ernst Roos , Ruud Brekelmans , Wouter van Eekelen , Dick den Hertog , Johan van Leeuwaarden