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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…

Statistics Theory · Mathematics 2026-02-26 Nahom Seyoum

In this work, we investigate an optimization problem over adapted couplings between pairs of real valued random variables, possibly describing random times. We relate those couplings to a specific class of causal transport plans between…

Probability · Mathematics 2022-10-18 Rémi Lassalle

Small sample sizes are common in many disciplines, which necessitates pooling roughly similar datasets across multiple institutions to study weak but relevant associations between images and disease outcomes. Such data often manifest…

Machine Learning · Computer Science 2024-11-19 Sotirios Panagiotis Chytas , Vishnu Suresh Lokhande , Peiran Li , Vikas Singh

For a sequence $\{X_{n}, \, n \geqslant 1 \}$ of nonnegative random variables where $\max[\min(X_{n} - s,t),0]$, $t > s \geqslant 0$, satisfy a moment inequality, sufficient conditions are given under which $\sum_{k=1}^n (X_k - \mathbb{E}…

Probability · Mathematics 2020-11-23 João Lita da Silva

In observational studies, propensity scores are commonly estimated by maxi- mum likelihood but may fail to balance high-dimensional pre-treatment covariates even after specification search. We introduce a general framework that unifies and…

Methodology · Statistics 2017-03-22 Qingyuan Zhao

This paper presents concentration inequalities and laws of large numbers under weak assumptions of irrelevance, expressed through lower and upper expectations. The results are variants and extensions of De Cooman and Miranda's recent…

Probability · Mathematics 2009-08-18 Fabio Gagliardi Cozman

The effect that weighted summands have on each other in approximations of $S=w_1S_1+w_2S_2+\cdots+w_NS_N$ is investigated. Here, $S_i$'s are sums of integer-valued random variables, and $w_i$ denote weights, $i=1,\dots,N$. Two cases are…

Probability · Mathematics 2018-06-12 Vydas Čekanavičius , Palaniappan Vellaisamy

New Vapnik and Chervonenkis type concentration inequalities are derived for the empirical distribution of an independent random sample. Focus is on the maximal deviation over classes of Borel sets within a low probability region. The…

Statistics Theory · Mathematics 2022-04-26 Stéphane Lhaut , Anne Sabourin , Johan Segers

Consider $n$ players whose "scores" are independent and identically distributed values $\{X_i\}_{i=1}^n$ from some discrete distribution $F$. We pay special attention to the cases where (i) $F$ is geometric with parameter $p\to0$ and (ii)…

Probability · Mathematics 2012-04-12 Julia Eaton , Anant Godbole , Betsy Sinclair

In observational studies, the assumption of sufficient overlap (positivity) is fundamental for the identification and estimation of causal effects. Failing to account for this assumption yields inaccurate and potentially infeasible…

Methodology · Statistics 2025-04-07 Jaehyuk Jang , Suehyun Kim , Kwonsang Lee

In this work, the possibility of clustering correlated random variables was examined, both because of their mutual similarity and because of their similarity to the principal components. The k-means algorithm and spectral algorithms were…

Machine Learning · Computer Science 2019-09-10 Zenon Gniazdowski , Dawid Kaliszewski

We derive exact expressions for the mean value of Meyer-Wallach entanglement Q for localized random vectors drawn from various ensembles corresponding to different physical situations. For vectors localized on a randomly chosen subset of…

Quantum Physics · Physics 2011-11-09 O. Giraud , J. Martin , B. Georgeot

We describe Bayes factors based on z, t, $\chi^2$, and F statistics when non-local moment prior distributions are used to define alternative hypotheses. The non-local alternative prior distributions are centered on standardized effects. The…

Methodology · Statistics 2024-07-26 Saptati Datta , Rachael Shudde , Valen E. Johnson

We develop a unified theory to analyze the microcanonical ensembles with several constraints given by unbounded observables. Several interesting phenomena that do not occur in the single constraint case can happen under the multiple…

Probability · Mathematics 2019-01-24 Kyeongsik Nam

Bell's theorem shows that local measurements on entangled states give rise to correlations incompatible with local hidden variable models. The degree of quantum nonlocality is not maximal though, as there are even more nonlocal theories…

Quantum Physics · Physics 2018-12-26 Cristhiano Duarte , Samuraí Brito , Barbara Amaral , Rafael Chaves

There has been a wide interest to extend univariate and multivariate nonparametric procedures to clustered and hierarchical data. Traditionally, parametric mixed models have been used to account for the correlation structures among the…

Statistics Theory · Mathematics 2018-03-02 Jaakko Nevalainen , Denis Larocque , Hannu Oja , Ilkka Pörsti

We provide a sharp quantitative version of the Gaussian concentration inequality: for every $r>0$, the difference between the measure of the $r$-enlargement of a given set and the $r$-enlargement of a half-space controls the square of the…

Analysis of PDEs · Mathematics 2017-09-01 Marco Barchiesi , Vesa Julin

A detailed understanding of all effects and influences on higher-order correlations is essential. At low charged multiplicity, the effect of a nonpoissonian multiplicity distribution can significantly distort correlations. Evidently, the…

High Energy Physics - Experiment · Physics 2013-08-22 H. C. Eggers , B. Buschbeck

We derive novel concentration inequalities that bound the statistical error for a large class of stochastic optimization problems, focusing on the case of unbounded objective functions. Our derivations utilize the following key tools: 1) A…

Machine Learning · Statistics 2026-01-01 Jeremiah Birrell

It is well-known that assumptions of monotonicity in size-bias couplings may be used to prove simple, yet powerful, Poisson approximation results. Here we show how these assumptions may be relaxed, establishing explicit Poisson…

Probability · Mathematics 2019-01-30 Fraser Daly , Oliver Johnson