Related papers: Upper tails for arithmetic progressions revisited
For the problem of estimating lower tail and upper tail copulas, we propose two bootstrap procedures for approximating the distribution of the corresponding empirical tail copulas. The first method uses a multiplier bootstrap of the…
Several objects in the Extremes literature are special instances of max-stable random sup-measures. This perspective opens connections to the theory of random sets and the theory of risk measures and makes it possible to extend…
Two old conjectures from problem sections, one of which from SIAM Review, concern the question of finding distributions that maximize P(Sn <= t), where Sn is the sum of i.i.d. random variables X1, ..., Xn on the interval [0,1], satisfying…
This paper examines bounds on upper tails for cycle counts in $G_{n,p}$. For a fixed graph $H$ define $\xi_H= \xi_H^{n,p}$ to be the number of copies of $H$ in $G_{n,p}$. It is a much studied and surprisingly difficult problem to understand…
We establish some asymptotic expansions for infinite weighted convolution of distributions having regular varying tails. Various applications to statistics and probability are developed.
In this paper non-asymptotic exponential estimates are derived for the tail distribution of polynomial martingale differences in terms unconditional tails distributions of summands. Applications are considered in the theory of polynomials…
Probabilistic forecasts comprehensively describe the uncertainty in the unknown future outcome, making them essential for decision making and risk management. While several methods have been introduced to evaluate probabilistic forecasts,…
``Localization'' has proven to be a valuable tool in the Statistical Learning literature as it allows sharp risk bounds in terms of the problem geometry. Localized bounds seem to be much less exploited in the Stochastic Optimization…
In this paper non-asymptotic exponential estimates are derived for tail of maximum martingale distribution by naturally norming in the spirit of the classical Law of Iterated Logarithm. Key words: Martingales, exponential estimations,…
High-probability analysis of stochastic first-order optimization methods under mild assumptions on the noise has been gaining a lot of attention in recent years. Typically, gradient clipping is one of the key algorithmic ingredients to…
Empirical distributions have their in-sample maxima as natural censoring. We look at the "hidden tail", that is, the part of the distribution in excess of the maximum for a sample size of $n$. Using extreme value theory, we examine the…
Floating-point round-off errors are ubiquitous in numerically intensive programs arising in fields such as scientific computing and optimization. As floating-point errors potentially lead to unexpected and catastrophic program failures, one…
Heavy-tailed distributions are infamously difficult to estimate because their moments tend to infinity as the shape of the tail decay increases. Nevertheless, this study shows the utilization of a modified group of moments for estimating a…
We propose an analytical approach to the computation of tail probabilities of compound distributions whose individual components have heavy tails. Our approach is based on the contour integration method, and gives rise to a representation…
We consider an unconstrained continuous optimization problem where, in each iteration, gradient estimates may be arbitrarily corrupted with a probability greater than 1/2. Additionally, function value estimates may exhibit heavy-tailed…
Let $\{X(t),t\ge0\}$ be a centered Gaussian process and let $\gamma$ be a non-negative constant. In this paper we study the asymptotics of $P\{\underset{t\in [0,\mathcal{T}/u^\gamma]}\sup X(t)>u\}$ as $u\to\infty$, with $\mathcal{T}$ an…
We explore the use of higher-order tail area approximations for Bayesian simulation. These approximations give rise to an alternative simulation scheme to MCMC for Bayesian computation of marginal posterior distributions for a scalar…
We consider the large deviations at the order of the variance for the central value of a family of $L$-functions among the members with bounded discriminant. When there is an upper bound on an integer moment of the central value twisted by…
We establish an upper bound on the tails of a random variable that arises as a solution of a stochastic difference equation. In the non--negative case our bound is similar to a lower bound obtained by Goldie and Gr\"ubel in 1996.
Upper bounds for the probabilities $\mathbb{P}(F\geq \mathbb{E} F + r)$ and $\mathbb{P}(F\leq \mathbb{E} F - r)$ are proved, where $F$ is a certain component count associated with a random geometric graph built over a Poisson point process…