Publications related to Copula (probability theory)

Price Discrimination with Robust Beliefs

This paper considers the problem of second-degree price discrimination when the type distribution is unknown or imperfectly specified by means of an ambiguity set. As robustness measure we use a performance index, equivalent to relative regret, which quant ...

2023

On Randomized Trace Estimates for Indefinite Matrices with an Application to Determinants

Daniel Kressner, Alice Cortinovis

Randomized trace estimation is a popular and well-studied technique that approximates the trace of a large-scale matrix B by computing the average of x(T) Bx for many samples of a random vector X. Often, B is symmetric positive definite (SPD) but a number ...

2022

Max-infinitely divisible models and inference for spatial extremes

Emeric Rolland Georges Thibaud, Raphaël Huser

For many environmental processes, recent studies have shown that the dependence strength is decreasing when quantile levels increase. This implies that the popular max-stable models are inadequate to capture the rate of joint tail decay, and to estimate jo ...

WILEY2021

Inference on the Angular Distribution of Extremes

Claudio Andri Semadeni

The spectral distribution plays a key role in the statistical modelling of multivariate extremes, as it defines the dependence structure of multivariate extreme-value distributions and characterizes the limiting distribution of the relative sizes of the co ...

EPFL2020

On the probability distribution of the local times of diagonally operator-self-similar Gaussian fields with stationary increments

Thomas Mountford, Kamran Kalbasi

In this paper, we study the local times of vector-valued Gaussian fields that are 'diagonally operator-selfsimilar' and whose increments are stationary. Denoting the local time of such a Gaussian field around the spatial origin and over the temporal unit h ...

INT STATISTICAL INST2020

Simultaneous autoregressive models for spatial extremes

Emeric Rolland Georges Thibaud

Motivated by the widespread use of large gridded data sets in the atmospheric sciences, we propose a new model for extremes of areal data that is inspired by the simultaneous autoregressive (SAR) model in classical spatial statistics. Our extreme SAR model ...

WILEY2020

Extremal behaviour of aggregated data with an application to downscaling

Sebastian Engelke, Raphaël Gérard Théodore Michel Marie de Deloÿe et Fourcade de Fondeville

The distribution of spatially aggregated data from a stochastic process may exhibit tail behaviour different from that of its marginal distributions. For a large class of aggregating functionals we introduce the -extremal coefficient, which quantifies this ...

OXFORD UNIV PRESS2019

A Data-Driven Approach Based on Multivariate Copulas for Quantitative Risk Assessment of Concrete Dam

Zhenzhu Meng, Yating Hu, Chenfei Shao

Risk assessment of dam's running status is an important part of dam management. A data-driven method based on monitored displacement data has been applied in risk assessment, owing to its easy operation and real-time analysis. However, previous data-driven ...

2019

Semiparametric Bayesian Risk Estimation for Complex Extremes

Thomas Lugrin

Extreme events are responsible for huge material damage and are costly in terms of their human and economic impacts. They strike all facets of modern society, such as physical infrastructure and insurance companies through environmental hazards, banking an ...

EPFL2018

Modelling across extremal dependence classes

Anthony Christopher Davison, Jennifer Lynne Wadsworth, Jonathan A. Tawn

Different dependence scenarios can arise in multivariate extremes, entailing careful selection of an appropriate class of models. In bivariate extremes, the variables are either asymptotically dependent or are asymptotically independent. Most available sta ...

Wiley-Blackwell2017

Caching of Bivariate Gaussians with Non-Uniform Preference Probabilities

Michael Christoph Gastpar, Guillaume Jean Op 't Veld

Caching is technique that alleviates networks during peak hours by transmitting partial information before a request for any is made. We study this method in a lossy source coding setting with Gaussian databases. A good caching strategy minimizes the data ...

2017

Robust Bounds In Multivariate Extremes

Sebastian Engelke

Extreme value theory provides an asymptotically justified framework for estimation of exceedance probabilities in regions where few or no observations are available. For multivariate tail estimation, the strength of extremal dependence is crucial and it is ...

Institute of Mathematical Statistics2017

Bridging asymptotic independence and dependence in spatial extremes using Gaussian scale mixtures

Emeric Rolland Georges Thibaud, Raphaël Huser

Gaussian scale mixtures are constructed as Gaussian processes with a random variance. They have non-Gaussian marginals and can exhibit asymptotic dependence unlike Gaussian processes, which are asymptotically independent except in the case of perfect depen ...

Elsevier Sci Ltd2017

Robust Growth-Optimal Portfolios

Daniel Kuhn, Napat Rujeerapaiboon, Wolfram Wiesemann

The growth-optimal portfolio is designed to have maximum expected log-return over the next rebalancing period. Thus, it can be computed with relative ease by solving a static optimization problem. The growth-optimal portfolio has sparked fascination among ...

Informs2016

Likelihood estimators for multivariate extremes

Anthony Christopher Davison, Raphaël Huser

The main approach to inference for multivariate extremes consists in approximating the joint upper tail of the observations by a parametric family arising in the limit for extreme events. The latter may be expressed in terms of componentwise maxima, high t ...

Springer2016

Bayesian uncertainty management in temporal dependence of extremes

Anthony Christopher Davison, Thomas Lugrin, Jonathan A. Tawn

Both marginal and dependence features must be described when modelling the extremes of a stationary time series. There are standard approaches to marginal modelling, but long-and short-range dependence of extremes may both appear. In applications, an assum ...

Springer Verlag2016

Dimensionality Reduction in Dynamic Optimization under Uncertainty

Napat Rujeerapaiboon

Dynamic optimization problems affected by uncertainty are ubiquitous in many application domains. Decision makers typically model the uncertainty through random variables governed by a probability distribution. If the distribution is precisely known, then ...

EPFL2016

Mass distributions marginalized over per-event errors

Frédéric Guillaume Dupertuis

We present generalizations of the Crystal Ball function to describe mass peaks in which the per event mass resolution is unknown and marginalized over. The presented probability density functions are tested using a series of toy Monte Carlo samples generat ...

Elsevier Science Bv2014

Analysis of Discrete L2 Projection on Polynomial Spaces with Random Evaluations

Fabio Nobile, Giovanni Migliorati, Erik Gustaf Bogislaw Von Schwerin

We analyse the problem of approximating a multivariate function by discrete least-squares projection on a polynomial space starting from random, noise-free observations. An area of possible application of such technique is Uncertainty Quantification (UQ) f ...

2014

A Euclidean Likelihood Estimator for Bivariate Tail Dependence

Michal Warchol, Boris Oumow

The spectral measure plays a key role in the statistical modeling of multivariate extremes. Estimation of the spectral measure is a complex issue, given the need to obey a certain moment condition. We propose a Euclidean likelihood-based estimator for the ...

Taylor & Francis Inc2013