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In this paper non-asymptotic exact rearrangement invariant norm estimates are derived for the maximum distribution of the family elements of some rearrangement invariant (r.i.) space over unbounded measure in the entropy terms and in the…

Functional Analysis · Mathematics 2008-08-26 E. Ostrovsky , E. Rogover

In this article we establish exponential moment bounds, moment bounds in fractional order smoothness spaces, a uniform H\"older continuity in time, and strong convergence rates for a class of fully discrete exponential Euler-type numerical…

Probability · Mathematics 2021-11-02 Arnulf Jentzen , Felix Lindner , Primož Pušnik

We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…

Statistics Theory · Mathematics 2007-12-18 Jiming Jiang , Yihui Luan , You-Gan Wang

Upper exponential inequalities for the tail probabilities of the centered and normalized number of triangles in the Erd\"{o}s-R\'{e}nyi graph are obtained, where the probability of every edge is fixed. The result is formulated in terms of…

Probability · Mathematics 2022-03-21 Alexander Bystrov , Nadezhda Volodko

Let $M_n$ be the number of steps of the loop-erasure of a simple random walk on $\mathbb{Z}^2$ from the origin to the circle of radius $n$. We relate the moments of $M_n$ to $Es(n)$, the probability that a random walk and an independent…

Probability · Mathematics 2010-12-14 Martin T. Barlow , Robert Masson

The local Rademacher complexity framework is one of the most successful general-purpose toolboxes for establishing sharp excess risk bounds for statistical estimators based on the framework of empirical risk minimization. Applying this…

Statistics Theory · Mathematics 2022-02-24 Varun Kanade , Patrick Rebeschini , Tomas Vaskevicius

In this paper, we introduce a new two-parameter lifetime distribution, called the exponential-generalized truncated logarithmic (EGTL) distribution, by compounding the exponential and generalized truncated logarithmic distributions. Our…

Statistics Theory · Mathematics 2018-09-28 Mohieddine Rahmouni , Ayman Orabi

In this paper, we prove exponential tail bounds for canonical (or degenerate) $U$-statistics and $U$-processes under exponential-type tail assumptions on the kernels. Most of the existing results in the relevant literature often assume…

Statistics Theory · Mathematics 2025-04-22 Abhishek Chakrabortty , Arun K. Kuchibhotla

We derive moment and tail estimates for Gaussian chaoses of arbitrary order with values in Banach spaces. We formulate a conjecture regarding two-sided estimates and show that it holds in a certain class of Banach spaces including L_q…

Probability · Mathematics 2021-06-08 Radosław Adamczak , Rafał Latała , Rafał Meller

We study the Central Limit Theorem (CLT) in the so-called mixed (anisotropic) Lebesgue-Riesz spaces and tail behavior of normed sums of centered random independent variables (vectors) with values in these spaces.

Probability · Mathematics 2013-08-27 E. Ostrovsky , L. Sirota

The article studies the almost surely asymptotics of extreme values $\bar{\xi}_n = \max_{1\leq i \leq n} \xi_i$, where $ \xi , \xi_1 , \xi_2 , \ldots$ are discrete identically distributed random variables. One of the main results on this…

Probability · Mathematics 2025-03-27 Kateryna Akbash , Ivan Matsak

We use bias-reduced estimators of high quantiles, of heavy-tailed distributions, to introduce a new estimator of the mean in the case of infinite second moment. The asymptotic normality of the proposed estimator is established and checked,…

Methodology · Statistics 2014-05-09 Brahim Brahimi , Djamel Meraghni , Abdelhakim Necir , Djabrane Yahia

For measuring tail risk with scarce extreme events, extreme value analysis is often invoked as the statistical tool to extrapolate to the tail of a distribution. The presence of large datasets benefits tail risk analysis by providing more…

Methodology · Statistics 2023-12-18 Liujun Chen , Deyuan Li , Chen Zhou

This paper derives exponential tail bounds and polynomial moment inequalities for the spectral norm deviation of a random matrix from its mean value. The argument depends on a matrix extension of Stein's method of exchangeable pairs for…

Probability · Mathematics 2013-05-06 Daniel Paulin , Lester Mackey , Joel A. Tropp

The main focus of this work is the asymptotic behavior of mass-conservative homogeneous fragmentations. Considering the logarithm of masses makes the situation reminiscent of branching random walks. The standard approach is to study {\bf…

Probability · Mathematics 2010-09-30 Nathalie Krell , Alain Rouault

Programs with randomization constructs is an active research topic, especially after the recent introduction of martingale-based analysis methods for their termination and runtimes. Unlike most of the existing works that focus on proving…

Logic in Computer Science · Computer Science 2019-02-18 Satoshi Kura , Natsuki Urabe , Ichiro Hasuo

The notion of expectiles, originally introduced in the context of testing for homoscedasticity and conditional symmetry of the error distribution in linear regression, induces a law-invariant, coherent and elicitable risk measure that has…

Methodology · Statistics 2020-07-20 Simone A. Padoan , Gilles Stupfler

Let $X$ be an $n\times n$ symmetric random matrix with independent but non-identically distributed entries. The deviation inequalities of the spectral norm of $X$ with Gaussian entries have been obtained by using the standard concentration…

Probability · Mathematics 2023-08-22 Guozheng Dai , Zhonggen Su , Hanchao Wang

This article discusses modelling of the tail of a multivariate distribution function by means of a large deviation principle (LDP), and its application to the estimation of the probability of a multivariate extreme event from a sample of n…

Statistics Theory · Mathematics 2017-02-23 Cees de Valk

Let $X$, $X_1$, $X_2$, $...$ be i.i.d. random variables, and let $S_n=X_1+... + X_n$ be the partial sums and $M_n=\max_{k\le n}|S_k|$ be the maximum partial sums. We give the sufficient and necessary conditions for a kind of limit theorems…

Probability · Mathematics 2007-05-23 Li-Xin Zhang