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We introduce a nonresponse mechanism for multivariate missing data in which each study variable and its nonresponse indicator are conditionally independent given the remaining variables and their nonresponse indicators. This is a…
We use point processes theory to describe the asymptotic distribution of all upper order statistics for observations collected at renewal times. As a corollary, we obtain limiting theorems for corresponding extremal processes.
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…
Extreme events are unusual and rare large-amplitude fluctuations that occur can unexpectedly in nonlinear dynamical systems. Events above the extreme event threshold of the probability distribution of a nonlinear process characterize…
Flood quantile estimation is of great importance for many engineering studies and policy decisions. However, practitioners must often deal with small data available. Thus, the information must be used optimally. In the last decades, to…
We develop two models for the temporal evolution of extreme events of multivariate $k$th order Markov processes. The foundation of our methodology lies in the conditional extremes model of Heffernan & Tawn (2004), and it naturally extends…
An asymptotic model for extreme behavior of certain Markov chains is the "tail chain". Generally taking the form of a multiplicative random walk, it is useful in deriving extremal characteristics such as point process limits. We place this…
With nonignorable missing data, likelihood-based inference should be based on the joint distribution of the study variables and their missingness indicators. These joint models cannot be estimated from the data alone, thus requiring the…
Multivariate extreme value models are used to estimate joint risk in a number of applications, with a particular focus on environmental fields ranging from climatology and hydrology to oceanography and seismic hazards. The semi-parametric…
In this paper we study coupled fully non-local equations, where a linear non-local operator jointly acts on the time and space variables. We establish existence and uniqueness of the solution. A maximum principle is proved and used to…
We analyze the asymptotic behavior of sequences of random variables defined by an initial condition, a stationary and ergodic sequence of random matrices, and an induction formula involving multiplication is the so-called max-plus algebra.…
Consider the case that one observes a single time-series, where at each time t one observes a data record O(t) involving treatment nodes A(t), possible covariates L(t) and an outcome node Y(t). The data record at time t carries information…
In this paper, we discuss the emergence of extreme events in a parametrically driven non-polynomial mechanical system with a velocity-dependent potential. We confirm the occurrence of extreme events from the probability distribution…
We present a new algorithm for the statistical model checking of Markov chains with respect to unbounded temporal properties, such as reachability and full linear temporal logic. The main idea is that we monitor each simulation run on the…
We study the consistency and weak convergence of the conditional tail function and conditional Hill estimators under broad dependence assumptions for a heavy-tailed response sequence and a covariate sequence. Consistency is established…
There is an increasing interest to understand the dependence structure of a random vector not only in the center of its distribution but also in the tails. Extreme-value theory tackles the problem of modelling the joint tail of a…
Exceptional points are singularities in the spectrum of non-Hermitian systems in which several eigenvectors are linearly dependent and their eigenvalues are equal to each other. Usually it is assumed that the order of the exceptional point…
We study tail risk dynamics in high-frequency financial markets and their connection with trading activity and market uncertainty. We introduce a dynamic extreme value regression model accommodating both stationary and local unit-root…
We consider stationary time series $\{X_j, j \in Z\} whose finite dimensional distributions are regularly varying with extremal independence. We assume that for each $h \geq 1$, conditionally on $X_0$ to exceed a threshold tending to…
We analyze the extreme value dependence of independent, not necessarily identically distributed multivariate regularly varying random vectors. More specifically, we propose estimators of the spectral measure locally at some time point and…