17 research outputs found
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
Strong consistency of estimators in partially linear models for longitudinal data with mixing-dependent structure
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
The Bounded Law of the Iterated Logarithm for Weakly Dependent Random Variables with Values in a Type 2 Banach Space
Moment inequalities and the central limit theorem for integrals of random fields with mixing
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
Asymptotic variance of the self-intersections of stable random walks using Darboux-Wiener theory
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,