We derive Edgeworth-type expansions for Poisson stochastic integrals, based on cumulant operators defined by the Malliavin calculus. As a consequence we obtain Stein approximation bounds for stochastic integrals, which are based on third cumulants instead of the L3 norm term found in the literature. The use of the third cumulant results into a convergence rate faster than the classical Berry-Es...

In this paper, we obtain an explicit Berry-Esseen bound in the central limit theorem for nonlinear statistics with bounded differences. Some examples are provided as well.

We obtain estimates for the Kolmogorov distance to appropriately chosen gaussians, of linear functions $$\begin{aligned} \sum _{i\in [n]^d} \theta _i X_i \end{aligned}$$ random tensors $$\varvec{X}=\langle X_i:i\in [n]^d\rangle $$ which are symmetric and exchangeable, whose entries have bounded third moment vanish on diagonal indices. These expressed in terms intrinsic (and easily computable) p...

In many applications, the available data come from a sampling scheme that causes loss of information in terms of left truncation. In some cases, in addition to left truncation, the data are weakly dependent. In this paper we are interested in deriving the asymptotic normality as well as a Berry-Esseen type bound for the kernel density estimator of left truncated and weakly dependent data.

We obtain rates of convergence in limit theorems of partial sums Sn for certain sequences of dependent, identically distributed random variables, which arise naturally in statistical mechanics, in particular, in the context of the Curie-Weiss models. Under appropriate assumptions there exists a real number α, a positive real number μ, and a positive integer k such that (Sn − nα)/n converges wea...