Related papers: Bias correction in multivariate extremes
We use bias-reduced estimators of high quantiles, of heavy-tailed distributions, to introduce a new estimator of the mean in the case of infinite second moment. The asymptotic normality of the proposed estimator is established and checked,…
This paper introduces a copula-based model for independent but non-identically distributed data with heteroscedastic extremes marginal and changing tail dependence structures. We establish a unified framework for inference by proving the…
Extreme value theory offers a statistical framework for quantifying the risk of rare events, with the generalized Pareto (GP) distribution providing the canonical limit model for univariate threshold exceedances. In many applications,…
The study of multivariate extremes is dominated by multivariate regular variation, although it is well known that this approach does not provide adequate distinction between random vectors whose components are not always simultaneously…
A bivariate random vector can exhibit either asymptotic independence or dependence between the largest values of its components. When used as a statistical model for risk assessment in fields such as finance, insurance or meteorology, it is…
We investigate a family of discrete-time stationary processes defined by multiple stable integrals and renewal processes with infinite means. The model may exhibit behaviors of short-range or long-range dependence, respectively, depending…
We often seek to estimate the causal effect of an exposure on a particular outcome in both randomized and observational settings. One such estimation method is the covariate-adjusted residuals estimator, which was designed for individually…
Causal discovery in multivariate extremes is challenging because extreme observations are sparse, dependent, and often affected by latent common shocks. Existing approaches focus on undirected extremal dependence, require prior graph…
We define a new multivariate time series model by generalizing the ARMAX process in a multivariate way. We give conditions on stationarity and analyze local dependence and domains of attraction. As a consequence of the obtained result, we…
The concept of univariate Range Value-at-Risk, presented by Cont et al. (2010), is extended in the multidimensional setting. Traditional risk measures are not well suited when dealing with heavy-tail distributions and infinite tail…
Assessing the probability of occurrence of extreme events is a crucial issue in various fields like finance, insurance, telecommunication or environmental sciences. In a multivariate framework, the tail dependence is characterized by the…
We propose a novel probabilistic model to facilitate the learning of multivariate tail dependence of multiple financial assets. Our method allows one to construct from known random vectors, e.g., standard normal, sophisticated joint…
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…
We present a weighted estimator of the covariance and correlation in bipartite complex systems with a double layer of heterogeneity. The advantage provided by the weighted estimators lies in the fact that the unweighted sample covariance…
We address the problem of estimating the Weibull tail-coefficient which is the regular variation exponent of the inverse failure rate function. We propose a family of estimators of this coefficient and an associate extreme quantile…
Causal dependence modelling of multivariate extremes is intended to improve our understanding of the relationships amongst variables associated with rare events. Regular variation provides a standard framework in the study of extremes. This…
In adaptive clinical trials, the conventional end-of-trial point estimate of a treatment effect is prone to bias, that is, a systematic tendency to deviate from its true value. As stated in recent FDA guidance on adaptive designs, it is…
We establish sharp tail asymptotics for component-wise extreme values of bivariate Gaussian random vectors with arbitrary correlation between the components. We consider two scaling regimes for the tail event in which we demonstrate the…
For the estimation of cumulative link models for ordinal data, the bias-reducing adjusted score equations in \citet{firth:93} are obtained, whose solution ensures an estimator with smaller asymptotic bias than the maximum likelihood…
Selection bias arises when the probability that an observation enters a dataset depends on variables related to the quantities of interest, leading to systematic distortions in estimation and uncertainty quantification. For example, in…