Related papers: Limit theorems for sums of random variables with m…
Real space condensation is known to occur in stochastic models of mass transport in the regime in which the globally conserved mass density is greater than a critical value. It has been shown within models with factorised stationary states…
We describe a general reduction technique for analyzing learning algorithms that are subject to light-tailed (but not necessarily bounded) randomness, a scenario that is often the focus of theoretical analysis. We show that the analysis of…
We consider moderately trimmed sums of non-negative i.i.d. random variables. We show that for every distribution function there exists a proper moderate trimming such that for the trimmed sum a non-trivial strong law of large numbers holds.…
We study a generalization of the Random Energy Model to the case when the number of exponential factors varies at random. Also a relation between REM and the Erd"os-R'enyi limit theorem for maximums of partial sums is considered.
In this paper, we consider the problem of linear regression with heavy-tailed distributions. Different from previous studies that use the squared loss to measure the performance, we choose the absolute loss, which is capable of estimating…
We prove a central limit theorem for a sequence of random variables whose means are ambiguous and vary in an unstructured way. Their joint distribution is described by a set of measures. The limit is (not the normal distribution and is)…
Two approaches are suggested to the definition of asymmetric generalized Weibull distribution. These approaches are based on the representation of the two-sided Weibull distributions as variance-mean normal mixtures or more general…
We construct a new tail bound for the sum of independent random variables for situations in which the expected value of the sum is known and each random variable lies within a specified interval, which may be different for each variable.…
The estimation of asset return distributions is crucial for determining optimal trading strategies. In this paper we describe the constrained mixture model, based on a mixture of Gamma and Gaussian distributions, to provide an accurate…
In this work we present concentration inequalities for the sum $S_n$ of independent integer-valued not necessary indentically distributed random variables, where each variable has tail function that can be bounded by some power function…
This paper deals with the extreme value analysis for the triangular arrays, which appear when some parameters of the mixture model vary as the number of observations grow. When the mixing parameter is small, it is natural to associate one…
There are many ways of establishing upper bounds on fluctuations of random variables, but there is no systematic approach for lower bounds. As a result, lower bounds are unknown in many important problems. This paper introduces a general…
We generalize and extend the recently proposed method to account for contributions of system size (or volume/participant) fluctuations to the experimentally measured moments of particle multiplicity distributions. We find that in the…
We offer a survey of recent results on covariance estimation for heavy-tailed distributions. By unifying ideas scattered in the literature, we propose user-friendly methods that facilitate practical implementation. Specifically, we…
Considerable literature has been devoted to developing statistical inferential results for risk measures, especially for those that are of the form of L-functionals. However, practical and theoretical considerations have highlighted quite a…
In this paper, we analyze the set of all possible aggregate distributions of the sum of standard uniform random variables, a simply stated yet challenging problem in the literature of distributions with given margins. Our main results are…
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 consider a multivariate heavy-tailed stochastic volatility model and analyze the large-sample behavior of its sample covariance matrix. We study the limiting behavior of its entries in the infinite-variance case and derive results for…
Multivariate rapid variation describes decay rates of joint light tails of a multivariate distribution. We impose a local uniformity condition to control decay variation of distribution tails along different directions, and using…
The statistical distribution of the ratio of two normal random variables is characterized by its heavy-tailed nature and absence of finite moments. The shape of its density function is highly variable, capable of exhibiting unimodal or…