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Related papers: Cram\'{e}r type moderate deviations for self-norma…

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We prove an asymptotic Cram\'er's theorem, that is, if the sequence $(X_{n}+ Y_{n})_{n\geq 1}$ converges in law to the standard normal distribution and for every $n\geq 1$ the random variables $X_{n}$ and $Y_{n}$ are independent, then…

Probability · Mathematics 2010-06-22 Ciprian Tudor

This letter aims at extending the Constrained Semiparametric Cramer-Rao Bound (CSCRB) for the joint estimation of mean vector and scatter matrix of Real Elliptically Symmetric (RES) distributions to Complex Elliptically Symmetric (CES)…

Signal Processing · Electrical Eng. & Systems 2019-02-26 Stefano Fortunati , Fulvio Gini , Maria S. Greco , Abdelhak M. Zoubir

This paper provides a finite sample bound for the error term in the Edgeworth expansion for a sum of independent, potentially discrete, nonlattice random vectors, using a uniform-in-$P$ version of the weaker Cram\'{e}r condition in Angst…

Statistics Theory · Mathematics 2019-08-14 Kyungchul Song

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

Stein's method is applied to obtain a general Cramer-type moderate deviation result for dependent random variables whose dependence is defined in terms of a Stein identity. A corollary for zero-bias coupling is deduced. The result is also…

Probability · Mathematics 2013-02-06 Louis H. Y. Chen , Xiao Fang , Qi-Man Shao

We perform a thorough analysis of the $\eta-\eta'$ mixing effects on the $\Lambda_b\rightarrow \Lambda \eta^{(')}$ decays based on the perturbative QCD (PQCD) factorization approach. Branching ratios, up-down and direct $CP$ asymmetries are…

High Energy Physics - Phenomenology · Physics 2023-06-02 Zhou Rui , Jia-Ming Li , Chao-Qi Zhang

We derive a Cram\'er-Rao lower bound for the variance of Floquet multiplier estimates that have been constructed from stable limit cycles perturbed by noise. To do so, we consider perturbed periodic orbits in the plane. We use a periodic…

Dynamical Systems · Mathematics 2017-11-30 Aurya Javeed

This paper studies the family of sliced Cram\'er metrics, quantifying their stability under distortions of the input functions. Our results bound the growth of the sliced Cram\'er distance between a function and its geometric deformation by…

Numerical Analysis · Mathematics 2025-10-03 William Leeb

We study the long-time behavior of the (critical) Kohn--Sham equation in two and three dimensions, i.e.,\[ \mathrm{i} \partial_t {\gamma} = \Big[-\frac{1}{2}\Delta + \lambda \, |\cdot|^{-1} \ast \rho_{{\gamma}} + \mu \,…

Analysis of PDEs · Mathematics 2026-05-29 Masaki Kawamoto , Jinyeop Lee , Changhun Yang , Chanjin You

In this paper we derive the moderate deviation principle for stationary sequences of bounded random variables under martingale-type conditions. Applications to functions of $\phi$-mixing sequences, contracting Markov chains, expanding maps…

Probability · Mathematics 2007-11-27 Jérôme Dedecker , Florence Merlevède , Magda Peligrad , Sergey Utev

We establish nonuniform Berry-Esseen bounds for martingales under the conditional Bernstein condition. These bounds imply Cram\'er type large deviations for moderate $x$'s, and are of exponential decay rate as de la Pe\~na's inequality when…

Probability · Mathematics 2017-08-03 Xiequan Fan , Ion Grama , Quansheng Liu

For $\Delta \ge 5$ and $q$ large as a function of $\Delta$, we give a detailed picture of the phase transition of the random cluster model on random $\Delta$-regular graphs. In particular, we determine the limiting distribution of the…

Probability · Mathematics 2021-09-16 Tyler Helmuth , Matthew Jenssen , Will Perkins

(This is the third version of a working paper.) We develop a family of self-normalized concentration inequalities for marginal mean under martingale-difference structure and $\phi/\tilde{\phi}$-mixing conditions, where the latter includes…

Statistics Theory · Mathematics 2025-12-17 Zihao Yuan

In this article, we discuss the sharp moderate and large deviations between the quantiles of population and the quantiles of samples. Cram\'{e}r type moderate deviations and Bahadur-Rao type large deviations are established with some mild…

Statistics Theory · Mathematics 2023-10-03 Xiequan Fan

We study shrinkage estimation of the mean parameters of a class of multivariate distributions for which the diagonal entries of the corresponding covariance matrix are certain quadratic functions of the mean parameter. This class of…

Statistics Theory · Mathematics 2022-07-04 Nikolas Siapoutis , Donald Richards , Bharath K. Sriperumbudur

This paper is aimed to study the ergodic short-term behaviour of discretizations of circle expanding maps. More precisely, we prove some asymptotics of the distance between the $t$-th iterate of Lebesgue measure by the dynamics $f$ and the…

Dynamical Systems · Mathematics 2023-08-09 Pierre-Antoine Guihéneuf , Maurizio Monge

Given n observations, we study the consistency of a batch of k new observations, in terms of their distribution function. We propose a non-parametric, non-likelihood test based on Edgeworth expansion of the distribution function. The…

Statistics Theory · Mathematics 2009-06-08 Mahendra Mariadassou , Avner Bar-Hen

We present precise moderate deviation probabilities, in both quenched and annealed settings, for a recurrent diffusion process with a Brownian potential. Our method relies on fine tools in stochastic calculus, including Kotani's lemma and…

Probability · Mathematics 2007-05-23 Yueyun Hu , Zhan Shi

In this paper we obtain a Bernstein type inequality for a class of weakly dependent and bounded random variables. The proofs lead to a moderate deviations principle for sums of bounded random variables with exponential decay of the strong…

Probability · Mathematics 2012-02-23 Florence Merlevède , Magda Peligrad , Emmanuel Rio

In this paper, we study self-normalized moderate deviations for degenerate { $U$}-statistics of order $2$. Let $\{X_i, i \geq 1\}$ be i.i.d. random variables and consider symmetric and degenerate kernel functions in the form…

Probability · Mathematics 2025-01-08 Lin Ge , Hailin Sang , Qi-Man Shao