Related papers: Weak convergence of weighted additive functionals …

Following Wiener, we consider the zeroes of Gaussian analytic functions in a strip in the complex plane, with translation-invariant distribution. We show that the variance of the number of zeroes in a long horizontal rectangle $[0,T]\times…

We consider the signed density of the extremal points of (two-dimensional) scalar fields with a Gaussian distribution. We assign a positive unit charge to the maxima and minima of the function and a negative one to its saddles. At first, we…

This paper deals with the Fisher-consistency, weak continuity and differentiability of estimating functionals corresponding to a class of both linear and nonlinear regression high breakdown M estimates, which includes S and MM estimates. A…

In this article, we investigate how the entrywise application of a non-linear function to symmetric orthogonally invariant random matrix ensembles alters the spectral distribution. We treat also the multivariate case where we apply…

Weak gravitational lensing surveys have the potential to directly probe mass density fluctuation in the universe. Recent studies have shown that it is possible to model the statistics of the convergence field at small angular scales by…

We propose another proof of the high dimensional spectrum convergence of the weighted sample covariance, more concise and self-sufficient but with stronger, but reasonable assumptions. We explain and illustrates this theorem for different…

Let $(X_k)_{k\geq1}$ be a Gaussian long-range dependent process with $EX_1=0$, $EX_1^2=1$ and covariance function $r(k)=k^{-D}L(k)$. For any measurable function $G$ let $(Y_k)_{k\geq1}=(G(X_k))_{k\geq1}$. We study the asymptotic behaviour…

We prove Central Limit Theorems and Stein-like bounds for the asymptotic behaviour of nonlinear functionals of spherical Gaussian eigenfunctions. Our investigation combine asymptotic analysis of higher order moments for Legendre polynomials…

This paper introduces a new framework to study the asymptotical behavior of the empirical distribution function (e.d.f.) of Gaussian vector components, whose correlation matrix $\Gamma^{(m)}$ is dimension-dependent. Hence, by contrast with…

In this paper we study the asymptotics of linear regression in settings with non-Gaussian covariates where the covariates exhibit a linear dependency structure, departing from the standard assumption of independence. We model the covariates…

In this paper we study the asymptotic behaviour via Gamma-convergence of some integral functionals which model some multi-dimensional structures and depend explicitly on the linearized strain tensor. The functionals are defined in…

We consider a generalization of the weighted random ball model. The model is driven by a random Poisson measure with a product heavy tailed intensity measure. Such a model typically represents the transmission of a network of stations with…

We study the behavior of the empirical distribution function of iterates of intermittent maps in the Hilbert space of square inegrable functions with respect to Lebesgue measure. In the long-range dependent case, we prove that the empirical…

We prove the reduction principle for asymptotics of functionals of vector random fields with weakly and strongly dependent components. These functionals can be used to construct new classes of random fields with skewed and heavy-tailed…

This paper addresses the asymptotics of functionals with linear growth depending on the Riesz $s$-fractional gradient on piecewise constant functions. We consider a general class of varying energy densities and, as $s\to 1$, we characterize…

We consider anisotropic self-similar random fields, in particular, the fractional Brownian sheet. This Gaussian field is an extension of fractional Brownian motion. We prove some properties of covariance function for self-similar fields…

We consider an estimation problem of expected functionals of a general random element that values in a metric space. If the functional forms an explicit function of some unknown parameters, we can estimate it by plugging-in a suitable…

Near-Gaussian probability densities are common in many important physical applications. Here we develop an asymptotic expansion methodology for computing entropic functionals for such densities. The expansion proposed is a close relative of…

We consider nonparametric functional regression when both predictors and responses are functions. More specifically, we let $(X_1,Y_1),...,(X_n,Y_n)$ be random elements in $\mathcal{F}\times\mathcal{H}$ where $\mathcal{F}$ is a semi-metric…

The Rosenblatt distribution plays a key role in the limit theorems for non-linear functionals of stationary Gaussian processes with long-range dependence. We derive new expressions for the characteristic function of the Rosenblatt…