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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

We derive convenient uniform concentration bounds and finite sample multivariate normal approximation results for quadratic forms, then describe some applications involving variance components estimation in linear random-effects models.…

Statistics Theory · Mathematics 2015-09-16 Lee H. Dicker , Murat A. Erdogdu

The asymptotic solution to the problem of comparing the means of two heteroscedastic populations, based on two random samples from the populations, hinges on the pivot underpinning the construction of the confidence interval and the test…

Statistics Theory · Mathematics 2017-10-26 Rajeshwari Majumdar , Suman Majumdar

Initially motivated by the study of the non-asymptotic properties of non-parametric tests based on permutation methods, concentration inequalities for uniformly permuted sums have been largely studied in the literature. Recently, Delyon et…

Probability · Mathematics 2018-05-10 Mélisande Albert

Covariate measurement error in nonparametric regression is a common problem in nutritional epidemiology and geostatistics, and other fields. Over the last two decades, this problem has received substantial attention in the frequentist…

Statistics Theory · Mathematics 2023-01-27 Shuang Zhou , Debdeep Pati , Tianying Wang , Yun Yang , Raymond J. Carroll

In this paper, a robust non-parametric measure of statistical dependence, or correlation, between two random variables is presented. The proposed coefficient is a permutation-like statistic that quantifies how much the observed sample S_n :…

Methodology · Statistics 2020-07-27 Rami Mahdi

We describe a previously unexplored effect of the continuous spontaneous localization model whereby a correlation develops in the distributions of two nearby non-interacting particles following a period of diffusion. We propose the use of…

Quantum Physics · Physics 2014-11-27 Daniel Bedingham

The extension of bivariate measures of dependence to non-Euclidean spaces is a challenging problem. The non-linear nature of these spaces makes the generalisation of classical measures of linear dependence (such as the covariance) not…

Statistics Theory · Mathematics 2024-10-10 Meshal Abuqrais , Davide Pigoli

The maximal correlation coefficient is a well-established generalization of the Pearson correlation coefficient for measuring non-linear dependence between random variables. It is appealing from a theoretical standpoint, satisfying…

Information Theory · Computer Science 2019-06-04 Elad Domanovitz , Uri Erez

In $M$-estimation under standard asymptotics, the weak convergence combined with the polynomial type large deviation estimate of the associated statistical random field Yoshida (2011) provides us with not only the asymptotic distribution of…

Statistics Theory · Mathematics 2017-04-18 Hiroki Masuda , Yusuke Shimizu

In observational studies with time-to-event outcomes, the g-formula can be used to estimate a treatment effect in the presence of confounding factors. However, the asymptotic distribution of the corresponding stochastic process is…

Statistics Theory · Mathematics 2024-04-26 Jasmin Rühl , Sarah Friedrich

A class of multivariate spectral representations for real-valued nonstationary random variables is introduced, which is characterised by a general complex Gaussian distribution. In this way, the temporal signal properties -- harmonicity,…

Signal Processing · Electrical Eng. & Systems 2020-07-29 Bruno Scalzo , Ljubisa Stankovic , Danilo P. Mandic

We derive simple concentration inequalities for bounded random vectors, which generalize Hoeffding's inequalities for bounded scalar random variables. As applications, we apply the general results to multinomial and Dirichlet distributions…

Probability · Mathematics 2013-11-05 Xinjia Chen

Nonprobability (convenience) samples are increasingly sought to reduce the estimation variance for one or more population variables of interest that are estimated using a randomized survey (reference) sample by increasing the effective…

We determine the asymptotic distribution of the sum of correlated variables described by a matrix product ansatz with finite matrices, considering variables with finite variances. In cases when the correlation length is finite, the law of…

Statistical Mechanics · Physics 2014-01-08 Florian Angeletti , Eric Bertin , Patrice Abry

We obtain non-asymptotic Gaussian concentration bounds for the difference between the invariant measure $\nu$ of an ergodic Brownian diffusion process and the empirical distribution of an approximating scheme with decreasing time step along…

Probability · Mathematics 2018-05-28 Igor Honoré , Stephane Menozzi , Gilles Pagès

We obtain a Bernstein type Gaussian concentration inequality for martingales. Our inequality improves the Azuma-Hoeffding inequality for moderate deviations $x$. Following the work of McDiarmid (1989), Talagrand (1996) and Boucheron, Lugosi…

Probability · Mathematics 2017-10-17 Xiequan Fan

The global clustering coefficient serves as a powerful metric for the structural analysis and comparison of complex networks. Random geometric graphs offer a realistic framework for representing the spatial constraints and geometry often…

Statistics Theory · Mathematics 2026-02-23 Mingao Yuan , Md. Niamul Islam Sium

We find the asymptotic distribution of the sample autocovariances of long-memory processes in cases of finite and infinite fourth moment. Depending on the interplay of assumptions on moments and the intensity of dependence, there are three…

Statistics Theory · Mathematics 2008-12-18 Lajos Horváth , Piotr Kokoszka

We consider sparse random intersection graphs with the property that the clustering coefficient does not vanish as the number of nodes tends to infinity. We find explicit asymptotic expressions for the correlation coefficient of degrees of…

Probability · Mathematics 2019-08-24 Mindaugas Bloznelis , Jerzy Jaworski , Valentas Kurauskas