Related papers: Exact bounds on the truncated-tilted mean, with ap…
An exact upper bound on the Winsorised-tilted mean of a symmetric random variable in terms of its second moment is given. Such results are used in work on nonuniform Berry--Esseen-type bounds for general nonlinear statistics.
Exact lower bounds on the exponential moments of min(y,X) and XI{X<y} are provided given the first two moments of a random variable X. These bounds are useful in work on large deviations probabilities and nonuniform Berry-Esseen bounds,…
An optimal bound on the quantiles of a certain kind of distributions is given. Such a bound is used in applications to Berry--Esseen-type bounds for nonlinear statistics.
A Berry-Esseen bound is obtained for self-normalized martingales under the assumption of finite moments. The bound coincides with the classical Berry-Esseen bound for standardized martingales. An example is given to show the optimality of…
This manuscript studies the Gaussian approximation of the coordinate-wise maximum of self-normalized statistics in high-dimensional settings. We derive an explicit Berry-Esseen bound under weak assumptions on the absolute moments. When the…
New Berry--Esseen-type bounds, with explicit constant factors, for the distribution of the Student statistic and, equivalently, for that of the self-normalized sum of independent zero-mean random variables are obtained. These bounds are…
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.
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 the best possible for many known statistics.…
Berry-Esseen-type bounds for total variation and relative entropy distances to the normal law are established for the sums of non-i.i.d. random variables.
We establish upper and lower bounds with matching leading terms for tails of weighted sums of two-sided exponential random variables. This extends Janson's recent results for one-sided exponentials.
Estimates are constructed for the deviation of the concentration functions of sums of independent random variables with finite variances from the folded normal distribution function without any assumptions concerning the existence of the…
This paper establishes the optimal sub-Gaussian variance proxy for truncated Gaussian and truncated exponential random variables. The proofs rely on first characterizing the optimal variance proxy as the unique solution to a set of two…
We present a general approach to the problem of determining tight asymptotic lower bounds for generalized central moments of the optimal alignment score of two independent sequences of i.i.d. random variables. At first, these are obtained…
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…
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,…
The stratified linear permutation statistic arises in various statistics problems, including stratified and post-stratified survey sampling, stratified and post-stratified experiments, conditional permutation tests, etc. Although we can…
Consider the task of generating samples from a tilted distribution of a random vector whose underlying distribution is unknown, but samples from it are available. This finds applications in fields such as finance and climate science, and in…
We establish a Berry--Esseen bound for general multivariate nonlinear statistics by developing a new multivariate-type randomized concentration inequality. The bound is the best possible for many known statistics. As applications,…
We establish nonuniform Berry-Esseen bounds for martingales under the conditional Bernstein condition. These bounds imply Cram\'er type large deviations for moderate $x$'s, and are of exponential decay rate as de la Pe\~na's inequality when…
Bounds of the accuracy of the normal approximation to the distribution of a sum of independent random variables are improved under relaxed moment conditions, in particular, under the absence of moments of orders higher than the second.…