Related papers: Sharp moment and exponential tail estimates for U-…
The note is devoted to estimates for convolutions appearing in some class of stochastic Volterra equations. Two maximal inequalities and exponential tail estimate are proved by the fractional method of infinite dimensional stochastic…
This work studies applications and generalizations of a simple estimation technique that provides exponential concentration under heavy-tailed distributions, assuming only bounded low-order moments. We show that the technique can be used…
We develop an efficient simulation algorithm for computing the tail probabilities of the infinite series $S = \sum_{n \geq 1} a_n X_n$ when random variables $X_n$ are heavy-tailed. As $S$ is the sum of infinitely many random variables, any…
We study the random variables (r.v.) with values in the so-called mixed (anisotropic) Lebesgue-Riesz spaces: formulate the sufficient conditions for belonging of the r.v. to these spaces, estimate the tail of norms distribution, especially…
We develop an unsupervised mixture model for non-negative, skewed and heavy-tailed data, such as losses in actuarial and risk management applications. The mixture has a lognormal component, which is usually appropriate for the body of the…
Low-rank tensor models are widely used in statistics. However, most existing methods rely heavily on the assumption that data follows a sub-Gaussian distribution. To address the challenges associated with heavy-tailed distributions…
Recently some papers, such as Aban, Meerschaert and Panorska (2006), Nuyts (2010) and Clark (2013), have drawn attention to possible truncation in Pareto tail modelling. Sometimes natural upper bounds exist that truncate the probability…
We study the almost surely finite random variable $S$ defined by the distributional fixed-point equation \[ S \stackrel{d}{=} 1 + \max\{US', (1-U)S''\}, \qquad U \sim \mathrm{Unif}(0,1), \] where $S'$ and $S''$ are independent copies of…
Different questions related with analysis of extreme values and outliers arise frequently in practice. To exclude extremal observations and outliers is not a good decision because they contain important information about the observed…
General upper tail estimates are given for counting edges in a random induced subhypergraph of a fixed hypergraph H, with an easy proof by estimating the moments. As an application we consider the numbers of arithmetic progressions and…
We investigate the use of optimization to compute bounds for extremal performance measures. This approach takes a non-parametric viewpoint that aims to alleviate the issue of model misspecification possibly encountered by conventional…
Let F be a distribution function with negative mean and regularly varying right tail. Under a mild smoothness condition we derive higher order asymptotic expansions for the tail distribution of the maxima of the random walk generated by F.…
Loynes' distribution, which characterizes the one dimensional marginal of the stationary solution to Lindley's recursion, possesses an ultimately exponential tail for a large class of increment processes. If one can observe increments but…
Several novel statistical methods have been developed to estimate large integrated volatility matrices based on high-frequency financial data. To investigate their asymptotic behaviors, they require a sub-Gaussian or finite high-order…
In several different fields, there is interest in analyzing the upper or lower tail quantile of the underlying distribution rather than mean or center quantile. However, the investigation of the tail quantile is difficult because of data…
We study the existence, strong consistency and asymptotic normality of estimators obtained from estimating functions, that are p-dimensional martingale transforms. The problem is motivated by the analysis of evolutionary clustered data,…
An important part of the legacy of Evarist Gin\'e is his fundamental contributions to our understanding of $U$-statistics and $U$-processes. In this paper we discuss the estimation of the mean of multivariate functions in case of possibly…
We establish sharp large-deviation asymptotic estimates for the maximum order statistic of i.i.d.\ standard normal random variables on all Borel subsets of the positive real line. This result yields more accurate tail approximations than…
We study the probability distribution of the maximum $M_S $ of a smooth stationary Gaussian field defined on a fractal subset $S$ of $\R^n$. Our main result is the equivalent of the asymptotic behavior of the tail of the distribution…
We present two-sided estimates of moments and tails of polynomial chaoses of order at most three generated by independent symmetric random variables with log-concave tails as well as for chaoses of arbitrary order generated by independent…