Related papers: An optimal bound on the quantiles of a certain kin…
We establish new lower bounds for the normal approximation in the Wasserstein distance of random variables that are functionals of a Poisson measure. Our results generalize previous findings by Nourdin and Peccati (2012, 2015) and Bierm\'e,…
Under correlation-type conditions, we derive upper bounds of order $\frac{1}{\sqrt{n}}$ for the Kolmogorov distance between the distributions of weighted sums of dependent summands and the normal law.
Known Bernstein-type upper bounds on the tail probabilities for sums of independent zero-mean sub-exponential random variables are improved in several ways at once. The new upper bounds have a certain optimality property.
A novel, non-trivial, probabilistic upper bound on the entropy of an unknown one-dimensional distribution, given the support of the distribution and a sample from that distribution, is presented. No knowledge beyond the support of the…
In this paper, we establish Berry--Esseen bounds for both self-normalized and non-self-normalized sums of locally dependent random variables. The proofs are based on Stein's method together with a concentration inequality approach. We…
An exchangeable pair approach is commonly taken in the normal and non-normal approximation using Stein's method. It has been successfully used to identify the limiting distribution and provide an error of approximation. However, when the…
We derive a Gaussian Central Limit Theorem for the sample quantiles based on locally dependent random variables with explicit convergence rate. Our approach is based on converting the problem to a sum of indicator random variables, applying…
We obtain Berry-Esseen-type bounds for the sum of random variables with a dependency graph and uniformly bounded moments of order $\delta \in (2,\infty]$ using a Fourier transform approach. Our bounds improve the state-of-the-art in the…
Let $\mu$ be a probability measure on $\text{GL}_d(\mathbb{R})$ and denote by $S_n:= g_n \cdots g_1$ the associated random matrix product, where $g_j$ are i.i.d. with law $\mu$. Under the assumptions that $\mu$ has a finite exponential…
We establish a general Berry-Esseen type bound which gives optimal bounds in many situations under suitable moment assumptions. By combining the general bound with Palm theory, we deduce a new error bound for assessing the accuracy of…
A Chernoff-type distribution is a nonnormal distribution defined by the slope at zero of the greatest convex minorant of a two-sided Brownian motion with a polynomial drift. While a Chernoff-type distribution is known to appear as the…
In this paper, we obtain the upper and lower bounds for two inequalities related to the range statistics. The first one is concerning the one-variable case and the second one is about the bivariate case.
Let $\mathbf{X}_1,...,\mathbf{X}_n$ be a random sample from a $p$-dimensional population distribution. Assume that $c_1n^{\alpha}\leq p\leq c_2n^{\alpha}$ for some positive constants $c_1,c_2$ and $\alpha$. In this paper we introduce a new…
New positivity bounds are derived for generalized (off-forward) parton distributions using the impact parameter representation. These inequalities are stable under the evolution to higher normalization points. The full set of inequalities…
Percentiles and more generally, quantiles are commonly used in various contexts to summarize data. For most distributions, there is exactly one quantile that is unbiased. For distributions like the Gaussian that have the same mean and…
Let $X_n=\sum_{i=1}^{\infty}a_i\epsilon_{n-i}$, where the $\epsilon_i$ are i.i.d. with mean 0 and at least finite second moment, and the $a_i$ are assumed to satisfy $|a_i|=O(i^{-\beta})$ with $\beta >1/2$. When $1/2<\beta<1$, $X_n$ is…
Bounds on the norm of quantum operators associated with classical Bell-type inequalities can be derived from their maximal eigenvalues. This quantitative method enables detailed predictions of the maximal violations of Bell-type…
We take another look at using Stein's method to establish uniform Berry-Esseen bounds for Studentized nonlinear statistics, highlighting variable censoring and an exponential randomized concentration inequality for a sum of censored…
We consider a process given as the solution of a stochastic differential equation with irregular, path dependent and time-inhomogeneous drift coefficient and additive noise. Explicit and optimal bounds for the Lebesgue density of that…
Applying Stein's method, an inductive technique and size bias coupling yields a Berry-Esseen theorem for normal approximation without the usual restriction that the coupling be bounded. The theorem is applied to counting the number of…