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Related papers: Cram\'er-type Moderate deviations under local depe…

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We define the local empirical process, based on $n$ i.i.d. random vectors in dimension $d$, in the neighborhood of the boundary of a fixed set. Under natural conditions on the shrinking neighborhood, we show that, for these local empirical…

Statistics Theory · Mathematics 2011-04-22 John H. J. Einmahl , Estáte V. Khmaladze

This paper deals with U-statistics of Poisson processes and multiple Wiener-It\^o integrals on the Poisson space. Via sharp bounds on the cumulants for both classes of random variables, moderate deviation principles, concentration…

Probability · Mathematics 2023-04-13 Matthias Schulte , Christoph Thaele

This paper introduces a new concept of stochastic dependence among many random variables which we call conditional neighborhood dependence (CND). Suppose that there are a set of random variables and a set of sigma algebras where both sets…

Statistics Theory · Mathematics 2018-06-06 Ji Hyung Lee , Kyungchul Song

We derive a Gaussian Central Limit Theorem for the sample quantiles based on locally dependent random variables with explicit convergence rate. Our approach is based on converting the problem to a sum of indicator random variables, applying…

Probability · Mathematics 2025-03-05 Partha S. Dey , Grigory Terlov

We derive a large deviation principle for families of random variables in the basin of attraction of spectrally positive stable distributions by proving a uniform version of the Tauberian theorem for Laplace-Stieltjes transforms. The main…

Probability · Mathematics 2026-05-25 Giampaolo Cristadoro , Gaia Pozzoli

Recent work in dynamic causal inference introduced a class of discrete-time stochastic processes that generalize martingale difference sequences and arrays as follows: the random variates in each sequence have expectation zero given certain…

Statistics Theory · Mathematics 2025-12-05 Walter Dempsey , Easton Huch

Stein's method is used to approximate sums of discrete and locally dependent random variables by a centered and symmetric Binomial distribution. Under appropriate smoothness properties of the summands, the same order of accuracy as in the…

Probability · Mathematics 2007-05-23 Adrian Röllin

We consider a stochastic differential equation and its Euler-Maruyama (EM) scheme, under some appropriate conditions, they both admit a unique invariant measure, denoted by $\pi$ and $\pi_\eta$ respectively ($\eta$ is the step size of the…

Probability · Mathematics 2021-09-09 Jianya Lu , Yuzhen Tan , Lihu Xu

We compute a variance lower bound for unbiased estimators in specified statistical models. The construction of the bound is related to the original Cram\'er-Rao bound, although it does not require the differentiability of the model.…

Statistics Theory · Mathematics 2012-04-13 Thibault Espinasse , Paul Rochet

We develop a maximum-likelihood based method for regression in a setting where the dependent variable is a random graph and covariates are available on a graph-level. The model generalizes the well-known $\beta$-model for random graphs by…

Methodology · Statistics 2017-05-24 Johan Wahlström , Isaac Skog , Patricio S. La Rosa , Peter Händel , Arye Nehorai

We show how a Cram\'er-Wold theorem for a family of multivariate probability distributions can be used to generate a similar theorem for mixtures (convex combinations) of distributions drawn from the same family. Using this abstract result,…

Probability · Mathematics 2025-06-06 Ricardo Fraiman , Leonardo Moreno , Thomas Ransford

An estimate of the order of approximation in the central limit theorem for strictly stationary associated random variables with finite moments of order q > 2 is obtained. A moderate deviation result is also obtained. We have a refinement of…

Probability · Mathematics 2017-09-19 M. Sreehari

We consider a stable but nearly unstable autoregressive process of any order. The bridge between stability and instability is expressed by a time-varying companion matrix $A_{n}$ with spectral radius $\rho(A_{n}) < 1$ satisfying…

Statistics Theory · Mathematics 2019-10-17 Frédéric Proïa

In this paper, we propose a new interpretation of local limit theorems for univariate and multivariate distributions on lattices. We show that - given a local limit theorem in the standard sense - the distributions are approximated well by…

Probability · Mathematics 2022-08-09 Michael Fleermann , Werner Kirsch , Gabor Toth

Given a random sample from a parametric model, we show how indirect inference estimators based on appropriate nonparametric density estimators (i.e., simulation-based minimum distance estimators) can be constructed that, under mild…

Statistics Theory · Mathematics 2011-01-10 Richard Nickl , Benedikt M. Pötscher

We investigate generalizations of the Cram\'er theorem. This theorem asserts that a Gaussian random variable can be decomposed into the sum of independent random variables if and only if they are Gaussian. We prove asymptotic counterparts…

Operator Algebras · Mathematics 2014-09-05 Solesne Bourguin , Jean-Christophe Breton

We extend previous large deviations results for the randomised Heston model to the case of moderate deviations. The proofs involve the G\"artner-Ellis theorem and sharp large deviations tools.

Pricing of Securities · Quantitative Finance 2020-05-06 Antoine Jacquier , Fangwei Shi

We study conditions under which treatment effect estimators constructed under the no-interference assumption in randomized experiments are asymptotically normal in the presence of interference. We prove that the standard Horvitz-Thompson…

Statistics Theory · Mathematics 2019-03-08 Alex Chin

We establish a quantitative normal approximation result for sums of random variables with multilevel local dependencies. As a corollary, we obtain a quantitative normal approximation result for linear functionals of random fields which may…

Probability · Mathematics 2019-05-27 Julian Fischer

In this paper, we propose a new approach to the investigation of asymptotic properties of trimmed $L$-statistics and we apply it to the Cram\'{e}r type large deviation problem. Our results can be compared with ones in Callaert et al.(1982)…

Probability · Mathematics 2019-04-23 Nadezhda Gribkova