Convergence of the Poincare Constant

The Poincare constant R(Y) of a random variable Y relates the L2 norm of a function g and its derivative g'. Since R(Y) - Var(Y) is positive, with equality if and only if Y is normal, it can be seen as a distance from the normal distribution. In this paper we establish a best possible rate of convergence of this distance in the Central Limit Theorem. Furthermore, we show that R(Y) is finite for discrete mixtures of normals, allowing us to add rates to the proof of the Central Limit Theorem in the sense of relative entropy.Comment: 11 page

Approximating the Reed-Frost epidemic process

The paper is concerned with refining two well-known approximations to the Reed–Frost epidemic process. The first is the branching process approximation in the early stages of the epidemic; we extend its range of validity, and sharpen the estimates of the error incurred. The second is the normal approximation to the distribution of the final size of a large epidemic, which we complement with a detailed local limit approximation. The latter, in particular, is relevant if the approximations are to be used for statistical inference

Rates in the strong invariance principle for ergodic automorphisms of the torus

30 pagesLet T be an ergodic automorphism of the d-dimensional torus. In the spirit of Le Borgne, we give conditions on the Fourier coeffi cients of a real valued function f under which the Birkhoff sums satis fy a strong invariance principle. Next, reinforcing the condition on the Fourier coeffi cients in a natural way, we obtain explicit rates of convergence in the strong invariance principle

Estimation of Mean and Covariance Operator for Banach Space Valued Autoregressive Processes with Dependent Innovations

mixing conditions, autoregressive process, Banach space, sample mean, empirical covariance,