Related papers: Measuring the magnitude of sums of independent ran…
We study how well moments of sums of independent symmetric random variables with logarithmically concave tails may be approximated by moments of Gaussian random variables.
In this paper we consider the problem of computing tail probabilities of the distribution of a random sum of positive random variables. We assume that the individual variables follow a reproducible natural exponential family (NEF)…
Using an intrinsic approach, we study some properties of random fields which appear as tail fields of regularly varying stationary random fields. The index set is allowed to be a general locally compact Hausdorff Abelian group $\mathbb{G}$.…
There is an increasing interest to understand the dependence structure of a random vector not only in the center of its distribution but also in the tails. Extreme-value theory tackles the problem of modelling the joint tail of a…
Measures of tail dependence between random variables aim to numerically quantify the degree of association between their extreme realizations. Existing tail dependence coefficients (TDCs) are based on an asymptotic analysis of relevant…
This article discusses modelling of the tail of a multivariate distribution function by means of a large deviation principle (LDP), and its application to the estimation of the probability of a multivariate extreme event from a sample of n…
We derive exponential tail inequalities for sums of random matrices with no dependence on the explicit matrix dimensions. These are similar to the matrix versions of the Chernoff bound and Bernstein inequality except with the explicit…
Handling multiplicity without losing much power has been a persistent challenge in various fields that often face the necessity of managing numerous statistical tests simultaneously. Recently, $p$-value combination methods based on…
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…
There are many ways of measuring and modeling tail-dependence in random vectors: from the general framework of multivariate regular variation and the flexible class of max-stable vectors down to simple and concise summary measures like the…
Identifying groups of variables that may be large simultaneously amounts to finding out which joint tail dependence coefficients of a multivariate distribution are positive. The asymptotic distribution of a vector of nonparametric,…
We present new explicit upper bounds for the smoothness of the distribution of the random diagonal sum $S_n=\sum_{j=1}^nX_{j,\pi(j)}$ of a random $n\times n$ matrix $X=(X_{j,r})$, where the $X_{j,r}$ are independent integer valued random…
Recently, the concept of tail dependence has been discussed in financial applications related to market or credit risk. The multivariate extreme value theory is a proper tool to measure and model dependence, for example, of large loss…
The distribution of the sum of independent identically distributed uniform random variables is well-known. However, it is sometimes necessary to analyze data which have been drawn from different uniform distributions. By inverting the…
We generalize a famous tail Doob's inequality, relative two non-negative random variables, arising in the martingale theory, in two directions: on the more general source data and on the random variables belonging to the so-called Grand…
Our work aims to study the tail behaviour of weighted sums of the form $\sum_{i=1}^{\infty} X_{i} \prod_{j=1}^{i}Y_{j}$, where $(X_{i}, Y_{i})$ are independent and identically distributed, with common joint distribution bivariate Sarmanov.…
Statistical significance measures the reliability of a result obtained from a random experiment. We investigate the number of repetitions needed for a statistical result to have a certain significance. In the first step, we consider…
The problem of estimating the coefficient of bivariate tail dependence is considered here from the robustness point of view; it combines two apparently contradictory theories of robust statistics and extreme value statistics. The usual…
Existing theory for multivariate extreme values focuses upon characterizations of the distributional tails when all components of a random vector, standardized to identical margins, grow at the same rate. In this paper, we consider the…
We obtain decay rates of probabilities of tails of polynomials in several independent random variables with heavy tails and derive stable limit theorems for nonconventional sums of such polynomials