Related papers: Effect of truncation on large deviations for heavy…
This paper is organized in three parts closely related to closure properties of heavy-tailed distributions and heavy-tailed random vectors. In the first part we consider two random variables X and Y with distributions F and G respectively.…
Estimating average treatment effects from observational data is challenging under practical violations of the positivity assumption. Targeted Maximum Likelihood Estimators (TMLEs) are widely used because of their double robustness and…
Randomised controlled trials in reproductive medicine are often subject to outcome truncation, where study outcomes are only defined in a subset of participants. Examples include birthweight (measurable only in the subgroup of participants…
We study in this paper the problem of least absolute deviation (LAD) regression for high-dimensional heavy-tailed time series which have finite $\alpha$-th moment with $\alpha \in (1,2]$. To handle the heavy-tailed dependent data, we…
Renewal processes with heavy-tailed power law distributed sojourn times are commonly encountered in physical modelling and so typical fluctuations of observables of interest have been investigated in detail. To describe rare events the rate…
Gaussian random vectors exhibit the loss of dimension phenomena, which relate to their joint survival tail behaviour. Besides, the fact that the components of such vectors are light-tailed complicates the approximations of various…
We consider weighted random balls in $\real^d$ distributed according to a random Poisson measure with heavy-tailed intensity and study the asymptotic behaviour of the total weight of some configurations in $\real^d$. This procedure amounts…
In this paper we propagate a large deviations approach for proving limit theory for (generally) multivariate time series with heavy tails. We make this notion precise by introducing regularly varying time series. We provide general large…
Probabilistic interpretation of transition from the dispersive transport regime to the quasi-Gaussian one in disordered semiconductors is given in terms of truncated Levy distributions. Corresponding transport equations with fractional…
We examine random variables in the power law/regularly varying class with stochastic tail exponent, the exponent $\alpha$ having its own distribution. We show the effect of stochasticity of $\alpha$ on the expectation and higher moments of…
We study the effect of single biased tracer particle in a bath of other particles performing the random average process (RAP) on an infinite line. We focus on the large time behavior of the mean and the fluctuations of the positions of the…
We present new estimators of the mean of a real valued random variable, based on PAC-Bayesian iterative truncation. We analyze the non-asymptotic minimax properties of the deviations of estimators for distributions having either a bounded…
Consider first passage percolation with identical and independent weight distributions and first passage time ${\rm T}$. In this paper, we study the upper tail large deviations $\mathbb{P}({\rm T}(0,nx)>n(\mu+\xi))$, for $\xi>0$ and $x\neq…
High-dimensional sparse modeling with censored survival data is of great practical importance, and several methods have been proposed for variable selection based on different models. However, the impact of biased sample caused by…
In this paper we propose a framework that enables the study of large deviations for point processes based on stationary sequences with regularly varying tails. This framework allows us to keep track not of the magnitude of the extreme…
In this paper we show an alternative approach to the concentration of truncated variation for stochastic processes on a real line. Our method is based on the moments control and can be used to generalize the results to the case of processes…
The coarsening and wavenumber selection of striped states growing from random initial conditions are studied in a non-relaxational, spatially extended, and far-from-equilibrium system by performing large-scale numerical simulations of…
We study how finite-window sampling (random spatial truncation) and reciprocal-space radial binning influence the detection of hyperuniformity in disordered systems. Using thirteen representative two-dimensional simulation systems (two…
We revisit the problem of condensation for independent, identically distributed random variables with a power-law tail, conditioned by the value of their sum. For large values of the sum, and for a large number of summands, a condensation…
For a fixed positive integer $\;k,\;$ limit laws of linearly normalized $\;k$-th upper order statistics are well known. In this article, a comprehensive study of tail behaviours of limit laws of normalized $k$-th upper order statistics…