Charles Suquet

Normal approximation for quasi-associated random fields

For quasi-associated random fields (comprising negatively and positively dependent fields) on we use Steins method to establish the rate of normal approximation for partial sums taken over arbitrary finite subsets of .

Estimating the edge of a Poisson process by orthogonal series

Let a homogeneous Poisson process with support delimited by the axis and the graph of a function f defined on [0, 1]. We study the asymptotical properties of a class of estimators of f obtained by the method of orthogonal functions. We give sufficient conditions for uniform convergences, we prove the asymptotical normality of the multivariate distributions and we find confidence intervals.

Invariance principles for adaptive self-normalized partial sums processes

Let [zeta]nse be the adaptive polygonal process of self-normalized partial sums Sk=[summation operator]1[less-than-or-equals, slant]i[less-than-or-equals, slant]kXi of i.i.d. random variables defined by linear interpolation between the points (Vk2/Vn2,Sk/Vn), k[less-than-or-equals, slant]n, where Vk2=[summation operator]i[less-than-or-equals, slant]k Xi2. We investigate the weak Holder convergence of [zeta]nse to the Brownian motion W. We prove particularly that when X1 is symmetric, [zeta]nse converges to W in each Holder space supporting W if and only if X1 belongs to the domain of attraction of the normal distribution. This contrasts strongly with Lampertis FCLT where a moment of X1 of order p>2 is requested for some Holder weak convergence of the classical partial sums process. We also present some partial extension to the nonsymmetric case.

L 2 (0,1) Weak Convergence of the Empirical Process for Dependent Variables

We consider the empirical process induced by dependent variables as a random element in L 2(0,1). Using some special properties of the Haar basis, we obtain a general tightness condition. In the strong mixing case, this allows us to improve on the well known result of Yoshihara (of course for theL 2 continuous functionals). In the same spirit, we give also an application to associated variables which improves a recent result of Yu. Some statistical applications are presented.

Hölder Versions of Banach Space Valued Random Fields

Abstract For rather general moduli of smoothness ρ, like ρ(ℎ)=ℎ α ln β (𝑐/ℎ), we consider the Hölder spaces H ρ (B) of functions [0,1] d → B is a separable Banach space. We establish an isomorphism between H ρ (B) and some sequence Banach space. With this analytical tool, we follow a very natural way to study, in terms of second differences, the existence of a version in H ρ (B) for a given random field.

Central Limit Theorems in Hölder Topologies for Banach Space Valued Random Fields

For rather general moduli of smoothness

Necessary and sufficient condition for the Lamperti invariance principle

\rho

OPERATOR FRACTIONAL BROWNIAN MOTION AS LIMIT OF POLYGONAL LINES PROCESSES IN HILBERT SPACE

, such as

Computing the distribution of sequential Hölder norms of the Brownian motion

\rho(h)=h^\alpha \log^\beta (c/h)

Hölderian Invariance Principles and Some Applications for Testing Epidemic Changes

, we consider the Holder spaces