Related papers: Modelling multivariate extremes through angular-ra…
Understanding variable dependence, particularly eliciting their statistical properties given a set of covariates, provides the mathematical foundation in practical operations management such as risk analysis and decision-making given…
Most extreme events in real life can be faithfully modeled as random realizations from a Generalized Pareto distribution, which depends on two parameters: the scale and the shape. In many actual situations, one is mostly concerned with the…
Regularly varying space-time processes have proved useful to study extremal dependence in space-time data. We propose a semiparametric estimation procedure based on a closed form expression of the extremogram to estimate parametric models…
Flexible distributions for modelling angular data have received considerable attention in recent years, with ongoing work extending existing circular models to provide greater flexibility in capturing diverse angular behaviours. In this…
We propose a probability distribution for multivariate binary random variables. The probability distribution is expressed as principal minors of the parameter matrix, which is a matrix analogous to the inverse covariance matrix in the…
Under general multivariate regular variation conditions, the extreme Value-at-Risk of a portfolio can be expressed as an integral of a known kernel with respect to a generally unknown spectral measure supported on the unit simplex. The…
Statistical modeling of a nonstationary spatial extremal dependence structure is challenging. Max-stable processes are common choices for modeling spatially-indexed block maxima, where an assumption of stationarity is usual to make…
Sparse linear regression -- finding an unknown vector from linear measurements -- is now known to be possible with fewer samples than variables, via methods like the LASSO. We consider the multiple sparse linear regression problem, where…
We introduce a new approach to a linear-circular regression problem that relates multiple linear predictors to a circular response. We follow a modeling approach of a wrapped normal distribution that describes angular variables and angular…
Multivariate regression techniques are commonly applied to explore the associations between large numbers of outcomes and predictors. In real-world applications, the outcomes are often of mixed types, including continuous measurements,…
Two dynamical indicators, the local dimension and the extremal index, used to quantify persistence in phase space have been developed and applied to different data across various disciplines. These are computed using the asymptotic limit of…
The goal of this paper is two-fold: 1. We review classical and recent measures of serial extremal dependence in a strictly stationary time series as well as their estimation. 2. We discuss recent concepts of heavy-tailed time series,…
We consider the problem of estimating parameters of stochastic differential equations (SDEs) with discrete-time observations that are either completely or partially observed. The transition density between two observations is generally…
An extremal model for the plasticity of amorphous materials is studied in a simple two-dimensional anti-plane geometry. The steady-state is analyzed through numerical simulations. Long-range spatial and temporal correlations in local slip…
Many existing approaches for estimating parameters in settings with distributional shifts operate under an invariance assumption. For example, under covariate shift, it is assumed that $p(y|x)$ remains invariant. We refer to such…
Accurate modelling of the joint extremal dependence structure within a stationary time series is a challenging problem that is important in many applications.\ Several previous approaches to this problem are only applicable to certain types…
Recently developed spatial capture-recapture (SCR) models represent a major advance over traditional capture-recapture (CR) models because they yield explicit estimates of animal density instead of population size within an unknown area.…
The stable-regenerative multiple-stable model has been shown recently to have distinct candidate extremal index and extremal index. To understand further this rare phenomenon, two more results are established here for the double-stable…
Multivariate problems are typically governed by anisotropic features such as edges in images. A common bracket of most of the various directional representation systems which have been proposed to deliver sparse approximations of such…
Statistical modeling of multivariate and spatial extreme events has attracted broad attention in various areas of science. Max-stable distributions and processes are the natural class of models for this purpose, and many parametric families…