Related papers: On the multivariate upcrossings index
The parameters of a discrete stationary Markov model are transition probabilities between states. Traditionally, data consist in sequences of observed states for a given number of individuals over the whole observation period. In such a…
In multivariate extreme value theory (MEVT), the focus is on analysis outside of the observable sampling zone, which implies that the region of interest is associated to high risk levels. This work provides tools to include directional…
Let \ell be the projected intersection local time of two independent Brownian paths in R^d for d=2,3. We determine the lower tail of the random variable \ell(U), where U is the unit ball. The answer is given in terms of intersection…
In one complex variable, the cross ratio is a well-known quantity associated with four given points in the complex plane that remains invariant under linear fractional maps. In particular, if one knows where three points in the complex…
In this paper we develop a very general class of bivariate discrete distributions. The basic idea is very simple. The marginals are obtained by taking the random geometric sum of a baseline distribution function. The proposed class of…
Inference over tails is performed by applying only the results of extreme value theory. Whilst such theory is well defined and flexible enough in the univariate case, multivariate inferential methods often require the imposition of…
We consider a stationary random field indexed by an increasing sequence of subsets of $\mathbb{Z}^d$ obeying a very broad geometrical assumption on how the sequence expands. Under certain mixing and local conditions, we show how the tail…
We introduce an index of convergence for double sequences of real numbers. This index is used to describe the behaviour of some bivariate interpolation sequences at points of discontinuity of the first kind. We consider in particular the…
In this paper, we develop a multistage approach for estimating the mean of a bounded variable. We first focus on the multistage estimation of a binomial parameter and then generalize the estimation methods to the case of general bounded…
In this paper we study an index of a critical orbit, defined in terms of the degree for invariant strongly indefinite functionals. We establish a relationship of this index with the index of a critical point of the mapping restricted to the…
For multivariate stationary time series many important properties, such as partial correlation, graphical models and autoregressive representations are encoded in the inverse of its spectral density matrix. This is not true for…
For statistical inference of means of stationary processes, one needs to estimate their time-average variance constants (TAVC) or long-run variances. For a stationary process, its TAVC is the sum of all its covariances and it is a multiple…
With the advent of ubiquitous monitoring and measurement protocols, studies have started to focus more and more on complex, multivariate and heterogeneous datasets. In such studies, multivariate response variables are drawn from a…
The accurate estimation of scaling exponents is central in the observational study of scale-invariant phenomena. Natural systems unavoidably provide observations over restricted intervals; consequently a stationary stochastic process (time…
This paper deals with the estimation of a sequence of frequencies from a corresponding sequence of signals. This problem arises in fields such as Doppler imaging where its specificity is twofold. First, only short noisy data records are…
A new notion of stochastic ordering is introduced to compare multivariate stochastic risk models with respect to extreme portfolio losses. In the framework of multivariate regular variation comparison criteria are derived in terms of…
Let ${\bf X}$ and ${\bf X}$ be two $n$-dimensional elliptical random vectors, we establish an identity for $E[f({\bf Y})]-E[f({\bf X})]$, where $f: \Bbb{R}^n \rightarrow \Bbb{R}$ fulfilling some regularity conditions. Using this identity we…
In this paper, we use Conley index theory to examine the Poincare index of an isolated invariant set. We obtain some limiting conditions on a critical point of a planar vector field to be an isolated invariant set. As a result we show the…
A new notion is introduced of matrix order indices which relate the matrix norm and its trace. These indices can be defined for any given matrix. They are especially important for matrices describing many-body systems, equilibrium as well…
We develop an early-warning signal for bifurcations of one-dimensional random difference equations with additive bounded noise, based on the asymptotic behaviour of the stationary density near a boundary of its support. We demonstrate the…