Related papers: Concentration inequalities for order statistics

In this paper, according to a certain criterion, we divide the exponential distribution class into three subclasses. One of them is closely related to the regular-variation-tailed distribution class, so it is called the…

We show, how the classical Berry-Esseen theorem for normal approximation may be used to derive rates of convergence for random sums of centerd, real-valued random variables with respect to a certain class of probability metrics, including…

Let X_1,X_2,... be a sequence of independent and identically distributed random variables, and put S_n=X_1+...+X_n. Under some conditions on the positive sequence tau_n and the positive increasing sequence a_n, we give necessary and…

The well-known "Janson's inequality" gives Poisson-like upper bounds for the lower tail probability \Pr(X \le (1-\eps)\E X) when X is the sum of dependent indicator random variables of a special form. We show that, for large deviations,…

In the setting where we have $n$ independent observations of a random variable $X$, we derive explicit error bounds in total variation distance when approximating the number of observations equal to the maximum of the sample (in the case…

We obtain bounds to quantify the distributional approximation in the delta method for vector statistics (the sample mean of $n$ independent random vectors) for normal and non-normal limits, measured using smooth test functions. For normal…

The bounds for absolute moments of order statistics are established. Let $X_1,\dots ,X_n$ be independent identically distributed real-valued random variables and let $X_{1:n}\le \dots \le X_{n:n}$ be the corresponding order statistics. The…

We study the effect of approximation errors in assessing the extreme behavior of heavy-tailed random objects. We give conditions for the approximation error such that the standard asymptotic results hold for the classical Hill estimator and…

Random matrices acting on structured sets play a fundamental role in high-dimensional geometry, compressed sensing, and randomized algorithms. Existing results primarily focus on subgaussian models, when random matrices act as…

In this article we review the standard versions of the Central and of the Levy-Gnedenko Limit Theorems, and illustrate their application to the convolution of independent random variables associated with the distribution known as…

We deduce the non-asymptotical (bilateral) estimates for moment inequalities for multiple sums of non-negative (more precisely, non-negative) independent random variables, on the other words, the well known U or V-statistics. Our…

In this paper, we establish novel concentration inequalities for additive functionals of geometrically ergodic Markov chains similar to Rosenthal inequalities for sums of independent random variables. We pay special attention to the…

The tails of the distribution of a mean zero, variance $\sigma^2$ random variable $Y$ satisfy concentration of measure inequalities of the form $\mathbb{P}(Y \ge t) \le \exp(-B(t))$ for $$ B(t)=\frac{t^2}{2( \sigma^2 + ct)} \quad \mbox{for…

We derive, up to a constant factor, matching lower and upper bounds on the concentration functions of suprema of separable centered Gaussian processes and order statistics of Gaussian random fields. These bounds reveal that suprema of…

This paper addresses the following question: given a sample of i.i.d. random variables with finite variance, can one construct an estimator of the unknown mean that performs nearly as well as if the data were normally distributed? One of…

Consider a pair of cumulative distribution functions $F$ and $G$, where $F$ is unknown and $G$ is a known reference distribution. Given a sample from $F$, we propose tests to detect the convexity or the concavity of $G^{-1}\circ F$ versus…

We present new concentration of measure inequalities for Markov chains, generalising results for chains that are contracting in Wasserstein distance. These are particularly suited to establishing the cut-off phenomenon for suitable chains.…

We establish a general inequality on the Poisson space, yielding an upper bound for the distance in total variation between the law of a regular random variable with values in the integers and a Poisson distribution. Several applications…

Rank 1 inhomogeneous random graphs are a natural generalization of Erd\H{o}s R\'enyi random graphs. In this generalization each node is given a weight. Then the probability that an edge is present depends on the product of the weights of…

Let $X$ be an $n$-dimensional random centered Gaussian vector with independent but not identically distributed coordinates and let $T$ be an orthogonal trasformation of $\mathbb R^n$. We show that the random vector $Y=T(X)$ satisfies…