Related papers: The integrated periodogram of a dependent extremal…
We study the weak convergence of conditional empirical copula processes, when the conditioning event has a nonzero probability. The validity of several bootstrap schemes is stated, including the exchangeable bootstrap. We define general -…
Modelling the extremal dependence of bivariate variables is important in a wide variety of practical applications, including environmental planning, catastrophe modelling and hydrology. The majority of these approaches are based on the…
A conditioned stochastic process can display a very different behavior from the unconditioned process. In particular, a conditioned process can exhibit non-Gaussian fluctuations even if the unconditioned process is Gaussian. In this work,…
We consider the Bouchaud trap model on the integers in the case that the trap distribution has a slowly varying tail at infinity. Our main result is a functional limit theorem for the model under the annealed law, analogous to the…
We explore the dependence structure in the sampled sequence of large networks. We consider randomized algorithms to sample the nodes and study extremal properties in any associated stationary sequence of characteristics of interest like…
Extremal graphical models encode the conditional independence structure of multivariate extremes. Key statistics for learning extremal graphical structures are empirical extremal variograms, for which we prove non-asymptotic concentration…
In this paper we consider a dynamic Erd\H{o}s-R\'{e}nyi random graph with independent identically distributed edge processes. Our aim is to describe the joint evolution of the entries of a subgraph count vector. The main result of this…
We study two-state (dichotomous, telegraph) random ergodic continuous-time processes with dynamics depending on their past. We take into account the history of process in an explicit form by introducing an integral non-local memory term…
Violation of the assumptions underlying classical (Gaussian) limit theory often yields unreliable statistical inference. This paper shows that the bootstrap can detect such violations by delivering simple and powerful diagnostic tests that…
We extend to Lipschitz continuous functionals either of the true paths or of the Euler scheme with decreasing step of a wide class of Brownian ergodic diffusions, the Central Limit Theorems formally established for their marginal empirical…
Let $(X_{\underline{\ell}})_{\underline{\ell} \in \mathbb Z^d}$ be a real random field (r.f.) indexed by $\mathbb Z^d$ with common probability distribution function $F$. Let $(z_k)_{k=0}^\infty$ be a sequence in $\mathbb Z^d$. The empirical…
We refer by threshold Ornstein-Uhlenbeck to a continuous-time threshold autoregressive process. It follows the Ornstein-Uhlenbeck dynamics when above or below a fixed level, yet at this level (threshold) its coefficients can be…
There is a wide literature on change point tests, but the case of variables with infinite variances is essentially unexplored. In this paper we address this problem by studying the asymptotic behavior of trimmed CUSUM statistics. We show…
The validity of various bootstrapping methods has been proved for the sample mean of strongly mixing data. But in many applications, there appear nonlinear statistics of processes that are not strongly mixing. We investigate the…
Randomly coupled Ising spins constitute the classical model of collective phenomena in disordered systems, with applications covering ferromagnetism, combinatorial optimization, protein folding, stock market dynamics, and social dynamics.…
The current understanding of pinned Brownian bridges is based on the Onsager-Machlup (OM) functional. The continuous-time limit of the OM functional can be expressed either by using the Fokker-Planck equation or by using the Radon-Nikodym…
We obtain an almost sure bound for oscillation rates of empirical distribution functions for stationary causal processes. For short-range dependent processes, the oscillation rate is shown to be optimal in the sense that it is as sharp as…
We consider the Pickands process {equation*} P_{n}(s)=\log (1/s)^{-1}\log \frac{X_{n-k+1,n}-X_{n-[k/s]+1,n}}{% X_{n-[k/s]+1,n}-X_{n-[k/s^{2}]+1,n}}, {equation*} {equation*} (\frac{k}{n}\leq s^2 \leq 1), {equation*} which is a generalization…
Recurrent event data are common in clinical studies when participants are followed longitudinally, and are often subject to a terminal event. With the increasing popularity of large pragmatic trials with a heterogeneous source population,…
In many contexts such as queuing theory, spatial statistics, geostatistics and meteorology, data are observed at irregular spatial positions. One model of this situation involves considering the observation points as generated by a Poisson…