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This paper is concerned with the limiting spectral behaviors of large dimensional Kendall's rank correlation matrices generated by samples with independent and continuous components. We do not require the components to be identically…

Statistics Theory · Mathematics 2019-12-16 Zeng Li , Qinwen Wang , Runze Li

The multivariate central limit theorems (CLT) for the volumes of excursion sets of stationary quasi-associated random fields on $\mathbb{R}^d$ are proved. Special attention is paid to Gaussian and shot noise fields. Formulae for the…

Probability · Mathematics 2012-03-02 Alexander Bulinski , Evgeny Spodarev , Florian Timmermann

We develop a central limit theorem (CLT) for a non-parametric estimator of the transition matrices in controlled Markov chains (CMCs) with finite state-action spaces. Our results establish precise conditions on the logging policy under…

Statistics Theory · Mathematics 2026-03-26 Ziwei Su , Imon Banerjee , Diego Klabjan

The deleting items theorems of weak law of large numbers (WLLN),strong law of large numbers (SLLN) and central limit theorem (CLT) are derived by substituting partial sum of random variable sequence with deleting items partial sum. We…

Probability · Mathematics 2019-08-12 Jingwei Liu

General Central limit theorem deals with weak limits (in type) of sums of row-elements of array random variables. In some situations as in the invariance principle problem, the sums may include only parts of the row-elements. For strictly…

In this paper, we obtain the central limit theorems for LS estimator in simple linear errors-in-variables (EV) regression models under some mild conditions. And we also show that those conditions are necessary in some sense.

Probability · Mathematics 2007-05-23 Yu Miao , Guangyu Yang , Luming Shen

We analyze the fluctuations of incomplete $U$-statistics over a triangular array of independent random variables. We give criteria for a Central Limit Theorem (CLT, for short) to hold in the sense that we prove that an appropriately scaled…

Probability · Mathematics 2020-03-24 Matthias Löwe , Sara Terveer

We consider "randomized" statistics constructed by using a finite number of observations a random field at randomly chosen points. We generalize the invariance principle (the functional CLT), the Glivenko--Cantelli theorem, the theorem…

Probability · Mathematics 2022-07-19 Youri Davydov , Arkady Tempelman

We give an overview of various results and methods related to information-theoretic distances of R\'enyi type in the light of their applications to the central limit theorem (CLT). The first part (Sections 1-9) is devoted to the total…

Information Theory · Computer Science 2025-03-07 S. G. Bobkov , G. P. Chistyakov , F. Götze

This paper provides a Central Limit Theorem (CLT) for a process $\{\theta_n, n\geq 0\}$ satisfying a stochastic approximation (SA) equation of the form $\theta_{n+1} = \theta_n + \gamma_{n+1} H(\theta_n,X_{n+1})$; a CLT for the associated…

Probability · Mathematics 2013-09-13 Gersende Fort

We prove a central limit theorem for the length of the longest subsequence of a random permutation which follows one of a class of repeating patterns. This class includes every fixed pattern of ups and downs having at least one of each,…

Combinatorics · Mathematics 2024-09-25 Aaron Abrams , Eric Babson , Henry Landau , Zeph Landau , James Pommersheim

We present a central limit theorem for stationary random fields that are short-range dependent and asymptotically independent. As an application, we present a central limit theorem for an infinite family of interacting It\^o-type diffusion…

Probability · Mathematics 2021-10-19 Le Chen , Davar Khoshnevisan , David Nualart , Fei Pu

Let $(X_i)_{i \geq 1}$ and $(Y_i)_{i\geq1}$ be two independent sequences of independent identically distributed random variables taking their values in a common finite alphabet and having the same law. Let $LC_n$ be the length of the…

Probability · Mathematics 2023-01-09 Christian Houdré , Ümit Işlak

We present a general methodology to construct triplewise independent sequences of random variables having a common but arbitrary marginal distribution $F$ (satisfying very mild conditions). For two specific sequences, we obtain in closed…

Statistics Theory · Mathematics 2022-05-25 Guillaume Boglioni Beaulieu , Pierre Lafaye de Micheaux , Frédéric Ouimet

The paper deals with a random connection model, a random graph whose vertices are given by a homogeneous Poisson point process on $\mathbb{R}^d$, and edges are independently drawn with probability depending on the locations of the two end…

Probability · Mathematics 2021-02-18 Van Hao Can , Khanh Duy Trinh

The purpose of this paper is to provide a first class of explicit sufficient conditions for the central limit theorem and related results in the setup of non-uniformly (partially) expanding non iid random transformations, considered as…

Dynamical Systems · Mathematics 2023-07-25 Yeor Hafouta

We prove quenched versions of (i) a large deviations principle (LDP), (ii) a central limit theorem (CLT), and (iii) a local central limit theorem (LCLT) for non-autonomous dynamical systems. A key advance is the extension of the spectral…

Dynamical Systems · Mathematics 2018-02-14 Davor Dragicevic , Gary Froyland , Cecilia Gonzalez-Tokman , Sandro Vaienti

A central limit theorem is established for a sum of random variables belonging to a sequence of random fields. The fields are assumed to have zero mean conditional on the past history and to satisfy certain conditional $\alpha$-mixing…

Probability · Mathematics 2024-09-17 Abdollah Jalilian , Arnaud Poinas , Ganggang Xu , Rasmus Waagepetersen

Recently a new type of central limit theorem for belief functions was given in Epstein et al. [9]. In this paper, we generalize the central limit theorem in Epstein et al. [9] to accommodate general bounded random variables. These results…

Probability · Mathematics 2017-12-21 Xiaomin Shi

The Generalized Central Limit Theorem is a remarkable generalization of the Central Limit Theorem, showing that the sum of a large number of independent, identically-distributed (i.i.d) random variables with infinite variance may converge…

Statistical Mechanics · Physics 2020-02-19 Ariel Amir