Related papers: Subgaussian Tail Bounds via Stability Arguments
Li and Hu recently established variance-type O(1/n) bounds for the sample mean of independent random vectors under sublinear expectations. We extend their results to the exponential concentration regime. For bounded, independent R^d-valued…
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…
Turbulent flows are notoriously difficult to describe and understand based on first principles. One reason is that turbulence contains highly intermittent bursts of vorticity and strain-rate with highly non-Gaussian statistics.…
The sums and maxima of weighted non-stationary random length sequences of regularly varying random variables may have the same tail and extremal indices, Markovich and Rodionov (2020). The main constraints are that there exists a unique…
For a discrete time Markov chain and in line with Strotz' consistent planning we develop a framework for problems of optimal stopping that are time-inconsistent due to the consideration of a non-linear function of an expected reward. We…
We discuss the possibilities and limitations of estimating the mean of a real-valued random variable from independent and identically distributed observations from a non-asymptotic point of view. In particular, we define estimators with a…
Under the assumption that the distribution of a nonnegative random variable $X$ admits a bounded coupling with its size biased version, we prove simple and strong concentration bounds. In particular the upper tail probability is shown to…
Nowadays in density estimation, posterior rates of convergence for location and location-scale mixtures of Gaussians are only known under light-tail assumptions; with better rates achieved by location mixtures. It is conjectured, but not…
Tail dependence plays an essential role in the characterization of joint extreme events in multivariate data. However, most standard tail dependence parameters assume continuous margins. This note presents a form of tail dependence suitable…
We present an estimate of the Wasserstein distance between the data distribution and the generation of score-based generative models. The sampling complexity with respect to dimension is $\mathcal{O}(\sqrt{d})$, with a logarithmic constant.…
The analysis of extremal dependence in high dimensions has recently attracted considerable interest. Existing methodology primarily focuses on modeling and estimation of extremal dependence structures, often supported by concentration…
The most popular approach in extreme value statistics is the modelling of threshold exceedances using the asymptotically motivated generalised Pareto distribution. This approach involves the selection of a high threshold above which the…
Change-plane regression identifies subpopulations through an interpretable linear threshold rule, but likelihood-based inference for the hard-threshold boundary is nonregular: objectives are non-smooth, the boundary is weakly identified…
We study concentration inequalities for structured weighted sums of random data, including (i) tensor inner products and (ii) sequential matrix sums. We are interested in tail bounds and concentration inequalities for those structured…
Tilt stability is a fundamental concept of variational analysis and optimization that plays a pivotal role in both theoretical issues and numerical computations. This paper investigates tilt stability of local minimizers for a general class…
This study presents a sampling-based method to guarantee robust stability of general control systems with uncertainty. The method allows the system dynamics and controllers to be represented by various data-driven models, such as Gaussian…
We describe methods for proving upper and lower bounds on infinite-time averages in deterministic dynamical systems and on stationary expectations in stochastic systems. The dynamics and the quantities to be bounded are assumed to be…
We introduce a new stochastic order for the tail dependence between random variables. We then study different measures of tail dependence which are monotone in the proposed order, thereby extending various known tail dependence coefficients…
We present upper and lower bounds for the tail distribution of the stationary waiting time $D$ in the stable $GI/GI/s$ FCFS queue. These bounds depend on the value of the traffic load $\rho$ which is the ratio of mean service and mean…
Let $X$ be a random variable with unknown mean and finite variance. We present a new estimator of the mean of $X$ that is robust with respect to the possible presence of outliers in the sample, provides tight sub-Gaussian deviation…