On weighted U-statistics for stationary random fields

Jana Klicnarová

Displaying similar documents to “On weighted U-statistics for stationary random fields”

Some limit behavior for linear combinations of order statistics

Yu Miao, Mengyao Ma (2021)

Kybernetika

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In the present paper, we establish the moderate and large deviations for the linear combinations of uniform order statistics. As applications, the moderate and large deviations for the $k$ -th order statistics from uniform distribution, Gini mean difference statistics and the $k$ -th order statistics from general continuous distribution are obtained.

Statistics of Random Processes I: General Theory. Statistics of Random Processes II: Applications - Liptser, R.S.; Shiryayev, A.M.

H. Heyer (1983)

Metrika

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Limit theorems for U-statistics indexed by a one dimensional random walk

Nadine Guillotin-Plantard, Véronique Ladret (2005)

ESAIM: Probability and Statistics

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Let ${(S_{n})}_{n \geq 0}$ be a $ℤ$ -random walk and ${(ξ_{x})}_{x \in ℤ}$ be a sequence of independent and identically distributed $ℝ$ -valued random variables, independent of the random walk. Let $h$ be a measurable, symmetric function defined on $ℝ^{2}$ with values in $ℝ$ . We study the weak convergence of the sequence $𝒰_{n}, n \in ℕ$ , with values in $D [0, 1]$ the set of right continuous real-valued functions with left limits, defined by $\sum_{i, j = 0}^{[n t]} h (ξ_{S_{i}}, ξ_{S_{j}}), t \in [0, 1] .$ Statistical applications are presented, in particular we prove a strong law of large numbers for...

Prediction problems

Nguyen Van Thu

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CONTENTSIntroduction......................................................................................................................................... 5I. Prediction of strictly stationary random fields.................................................................................... 6II. Prediction of stationary-in-norm fields in Banach spaces of random variables........................ 23 § 1. Banach spaces of random variables...................................................................................

On the existence and asymptotic behavior of the random solutions of the random integral equation with advancing argument

Henryk Gacki (1996)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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1. Introduction Random Integral Equations play a significant role in characterizing of many biological and engineering problems [4,5,6,7]. We present here new existence theorems for a class of integral equations with advancing argument. Our method is based on the notion of a measure of noncompactness in Banach spaces and the fixed point theorem of Darbo type. We shall deal with random integral equation with advancing argument $x (t, ω) = h (t, ω) + \int^{t + δ (t)} ₀ k (t, τ, ω) f (τ, x_{τ} (ω)) d τ$ , (t,ω) ∈ R⁺ × Ω, (1) where (i) (Ω,A,P) is a complete probability...

Two-parameter non-commutative Central Limit Theorem

Natasha Blitvić (2014)

Annales de l'I.H.P. Probabilités et statistiques

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In 1992, Speicher showed the fundamental fact that the probability measures playing the role of the classical Gaussian in the various non-commutative probability theories (viz. fermionic probability, Voiculescu’s free probability, and $q$ -deformed probability of Bożejko and Speicher) all arise as the limits in a generalized Central Limit Theorem. The latter concerns sequences of non-commutative random variables (elements of a $*$ -algebra equipped with a state) drawn from an ensemble of pair-wise...

Stress-strength based on $m$ -generalized order statistics and concomitant for dependent families

Filippo Domma, Abbas Eftekharian, Mostafa Razmkhah (2019)

Applications of Mathematics

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The stress-strength model is proposed based on the $m$ -generalized order statistics and the corresponding concomitant. For the dependency between $m$ -generalized order statistics and its concomitant, a bivariate copula expansion is considered and the stress-strength model is obtained for two special cases of order statistics and upper record values. In the particular case of copula function, the generalized Farlie-Gumbel-Morgenstern bivariate distribution function is considered with proportional...

Ballistic regime for random walks in random environment with unbounded jumps and Knudsen billiards

Francis Comets, Serguei Popov (2012)

Annales de l'I.H.P. Probabilités et statistiques

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We consider a random walk in a stationary ergodic environment in $ℤ$ , with unbounded jumps. In addition to uniform ellipticity and a bound on the tails of the possible jumps, we assume a condition of strong transience to the right which implies that there are no “traps.” We prove the law of large numbers with positive speed, as well as the ergodicity of the environment seen from the particle. Then, we consider Knudsen stochastic billiard with a drift in a random tube in $ℝ^{d}$ , $d \geq 3$ , which serves...

Comparison of order statistics in a random sequence to the same statistics with I.I.D. variables

Jean-Louis Bon, Eugen Păltănea (2006)

ESAIM: Probability and Statistics

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The paper is motivated by the stochastic comparison of the reliability of non-repairable $k$ -out-of- $n$ systems. The lifetime of such a system with nonidentical components is compared with the lifetime of a system with identical components. Formally the problem is as follows. Let $U_{i}, i = 1, . . ., n,$ be positive independent random variables with common distribution $F$ . For $λ_{i} > 0$ and $μ > 0$ , let consider $X_{i} = U_{i} / λ_{i}$ and $Y_{i} = U_{i} / μ, i = 1, . . ., n$ . Remark that this is no more than a change of scale for each term. For $k \in {1, 2, . . ., n},$ let us define $X_{k : n}$ to be the $k$ th order...

Further results on laws of large numbers for uncertain random variables

Feng Hu, Xiaoting Fu, Ziyi Qu, Zhaojun Zong (2023)

Kybernetika

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The uncertainty theory was founded by Baoding Liu to characterize uncertainty information represented by humans. Basing on uncertainty theory, Yuhan Liu created chance theory to describe the complex phenomenon, in which human uncertainty and random phenomenon coexist. In this paper, our aim is to derive some laws of large numbers (LLNs) for uncertain random variables. The first theorem proved the Etemadi type LLN for uncertain random variables being functions of pairwise independent...

Characterization of associate spaces of weighted Lorentz spaces with applications

Amiran Gogatishvili, Luboš Pick, Filip Soudský (2014)

Studia Mathematica

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We characterize associate spaces of weighted Lorentz spaces GΓ(p,m,w) and present some applications of this result including necessary and sufficient conditions for a Sobolev-type embedding into $L^{\infty}$ .

An invariance principle in $L^{2} [0, 1]$ for non stationary $ϕ$ -mixing sequences

Paulo Eduardo Oliveira, Charles Suquet (1995)

Commentationes Mathematicae Universitatis Carolinae

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Invariance principle in $L^{2} (0, 1)$ is studied using signed random measures. This approach to the problem uses an explicit isometry between $L^{2} (0, 1)$ and a reproducing kernel Hilbert space giving a very convenient setting for the study of compactness and convergence of the sequence of Donsker functions. As an application, we prove a $L^{2} (0, 1)$ version of the invariance principle in the case of $ϕ$ -mixing random variables. Our result is not available in the $D (0, 1)$ -setting.