Related papers: Sharp moment estimates for polynomial martingales
The aim of this paper is to propose new Rosenthal-type inequalities for moments of order higher than 2 of the maximum of partial sums of stationary sequences including martingales and their generalizations. As in the recent results by…
In this work, we focus on some conditional extreme risk measures estimation for elliptical random vectors. In a previous paper, we proposed a methodology to approximate extreme quantiles, based on two extremal parameters. We thus propose…
This paper obtains asymptotic results for parametric inference using prediction-based estimating functions when the data are high frequency observations of a diffusion process with an infinite time horizon. Specifically, the data are…
We consider non-convex stochastic optimization using first-order algorithms for which the gradient estimates may have heavy tails. We show that a combination of gradient clipping, momentum, and normalized gradient descent yields convergence…
We derive an equilibrated a posteriori error estimator for the space (semi) discretization of the scalar wave equation by finite elements. In the idealized setting where time discretization is ignored and the simulation time is large, we…
We present order of magnitude estimates for the quantiles of non-negative linear combinations of non-negative random variables, as well as deviation inequalities for general linear combinations of independent random variables, under the…
In a seminal paper Biggins and Kyprianou \cite{BKy04} proved the existence of a non degenerate limit for the {\it Derivative martingale} of the branching random walk. As shown in \cite{Aid11} and \cite{Mad11}, this is an object of central…
We consider positively supported Borel measures for which all moments exist. On the set of compactly supported measures in this class a partial order is defined via eventual dominance of the moment sequences. Special classes are identified…
Several convenient methods for calculation of fractional absolute moments are given with application to heavy tailed distributions. We use techniques of fractional differentiation to obtain formulae for $E[|X-\mu|^\gamma]$ with $1<\gamma<2$…
Hoeffding has shown that tail bounds on the distribution for sampling from a finite population with replacement also apply to the corresponding cases of sampling without replacement. (A special case of this result is that binomial tail…
Tail dependence models for distributions attracted to a max-stable law are fitted using observations above a high threshold. To cope with spatial, high-dimensional data, a rank-based M-estimator is proposed relying on bivariate margins…
Many stochastic continuous-state dynamical systems can be modeled as probabilistic programs with nonlinear non-polynomial updates in non-nested loops. We present two methods, one approximate and one exact, to automatically compute, without…
We consider estimation of the quadratic (co)variation of a semimartingale from discrete observations which are irregularly spaced under high-frequency asymptotics. In the univariate setting, results by Jacod (2008) are generalized to the…
Standard approaches to probabilistic reasoning require that one possesses an explicit model of the distribution in question. But, the empirical learning of models of probability distributions from partial observations is a problem for which…
We give a new framework for proving the existence of low-degree, polynomial approximators for Boolean functions with respect to broad classes of non-product distributions. Our proofs use techniques related to the classical moment problem…
We propose a mean functional which exists for any probability distributions, and which characterizes the Pareto distribution within the set of distributions with finite left endpoint. This is in sharp contrast to the mean excess plot which…
The paper compares probabilistic and exact methods for estimating the asymptotic behavior of summation arithmetic functions, and estimates of the results are obtained by precise methods. Conditions for stationarity in the broad sense are…
This paper considers inference for conditional moment inequality models using a multiscale statistic. We derive the asymptotic distribution of this test statistic and use the result to propose feasible critical values that have a simple…
In this paper, we study non-asymptotic deviation bounds of the least squares estimator in Gaussian AR($n$) processes. By relying on martingale concentration inequalities and a tail-bound for $\chi^2$ distributed variables, we provide a…
In this article, we introduce a conditional marginal model for longitudinal data, in which the residuals form a martingale difference sequence. This model allows us to consider a rich class of estimating equations, which contains several…