This paper deals with the quantitative normal approximation of non-linear functionals of Poisson random measures, where the quality is measured by the Kolmogorov distance. Combining Stein’s method with the Malliavin calculus of variations on the Poisson space, we derive a bound, which is strictly smaller than what is available in the literature. This is applied to sequences of multiple integral...

Some limit theorems (including a Berry-Esseen bound) are derived for the number of comparisons taken by the Boyer-Moore algorithm for finding the occurrences of a given pattern in a random Markovian text. Previously, only special variants of this algorithm have been analyzed. We also propose means of computing the limiting constants for the mean and the variance.

Refinements of first order asymptotic results axe reviewed, with a number of Ph.D. projects supervised by van Zwet serving as stepping stones. Berry-Esseen bounds and Edgeworth expansions are discussed for R-, Land [/-statistics. After these special classes, the question about a general second order theory for asymptotically normal statistics is addressed. As a final topic, empirical Edgeworth ...

Let T be a general sampling statistic that can be written as a linear statistic plus an error term. Uniform and non-uniform Berry-Esseen type bounds for T are obtained. The bounds are best possible for many known statistics. Applications to U-statistic, multi-sample U-statistic, L-statistic, random sums, and functions of non-linear statistics are discussed.

We obtain rates of convergence and asymptotic expansions in limit theorems for powers of reciprocals of random variables. Our results improve on recent work of Shapiro [18], who obtained Berry-Esseen bounds of order n~ l/9+c (e > 0). Under weaker conditions than Shapiro imposed we obtain asymptotic expansions whose first term is of order n~ i (logn) 2 .

We derive uniform and non–uniform error bounds in the normal approximation under a general dependence assumption. Our method is tailor made for dynamic time series models employed in the econometric literature but it is also applicable for many other dependent processes. Neither stationarity nor any smoothness conditions of the underlying distributions are required. If the introduced weak depen...

In this paper we study the estimation of a quantile function based on left truncated and right censored data by the kernel smoothing method. Asymptotic normality and a Berry-Esseen type bound for the kernel quantile estimator are derived. Monte Carlo studies are conducted to compare the proposed estimator with the PL-quantile estimator.

Associated to the Bergman kernels of a polarized toric \kahler manifold $(M, \omega, L, h)$ are sequences measures $\{\mu_k^z\}_{k=1}^{\infty}$ parametrized by points $z \in M$. For each $z$ in open orbit, we prove central limit theorem for $\mu_k^z$. The center mass $\mu_k^z$ is image under moment map; after re-centering at $0$ and dilating $\sqrt{k}$, re-normalized measure tends centered Gaus...

The central limit theorem is considered with respect to the transport distance W2. We discuss an alternative approach to a result of E. Rio, based on a Berry–Esseen-type bound for the entropic distance to the normal distribution. © 2013 Elsevier B.V. All rights reserved. Let X and Z be random variables with distributions F and G, having finite second moments. The Kantorovich distance W2(F ,G) b...