In this paper, the authors investigate the Berry-Esseen bounds of weighted kernel estimator for a nonparametric regression model based on linear process errors under a LNQD random variable sequence. The rate of the normal approximation is shown as [Formula: see text] under some appropriate conditions. The results obtained in the article generalize or improve the corresponding ones for mixing de...

We study the number of subtrees on the fringe of random recursive trees and random binary search trees whose limit law is known to be either normal or Poisson or degenerate depending on the size of the subtree. We introduce a new approach to this problem which helps us to further clarify this phenomenon. More precisely, we derive optimal Berry-Esseen bounds and local limit theorems for the norm...

This note provides a conditional Berry-Esseen bound for the sum of martingale difference sequence $\{X_i\}_{i=1}^n$ in $\mathbb{R}^d$, $d\ge 1$, adapted to filtration $\{\mathcal{F}_i\}_{i=1}^n$. We approximate distribution $S=\sum_{i=1}^n X_i$ given some $\sigma$-field $\mathcal{F}_0\subset \mathcal{F}_1$ by that mean-zero normal random vector having same variance $\mathcal{F}_0 $ as $S$. Assu...

We establish fundamental limits on estimation accuracy for the noisy 20 questions problem with measurement-dependent noise and introduce optimal non-adaptive procedures that achieve these limits. The minimal achievable resolution is defined as absolute difference between estimated true locations of a target over unit cube, given finite number queries constrained by excess-resolution probability...

Suppose that the (normalised) partial sum of a stationary sequence converges to standard normal random variable. Given sufficiently moments, when do we have rate convergence n−1∕2 in uniform metric, other words, optimal Berry-Esseen bound? We study this question quite general framework and find (almost) sharp dependence conditions. The result applies many different processes dynamical systems. ...

In this paper we investigate the speed of convergence of the fluctuations of a general class of Feynman-Kac particle approximation models. We design an original approach based on new Berry-Esseen type estimates for abstract martingale sequences combined with original exponential concentration estimates of interacting processes. These results extend the corresponding statements in the classical ...

We derive Berry-Esseen approximation bounds for general functionals of independent random variables, based on a continuous-time integration by parts setting and discrete chaos expansions methods. Our approach improves related results obtained in discrete-time settings applies to U-statistics satisfying the weak assumption decomposability Hoeffding sense, yield Kolmogorov distance instead Wasser...