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Almost sure convergence of extreme order statistics
Electronic Journal of Statistics, 2009 Submitted to the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org)
Saralees Nadarajah, Zuoxiang Peng
exaly +5 more sources
Almost Sure Convergence of Generalized $U$-Statistics
Annals of Probability, 1977 Almost sure convergence of generalized $U$-statistics and von Mises' differentiable statistical functions is studied with the help of the general $L \log L$ martingale convergence theorem.
exaly +4 more sources
Estimating Cumulative Distribution Function Using Gamma Kernel [PDF]
Journal of Sciences, Islamic Republic of Iran, 2022 In this article, we propose the gamma kernel estimator for the cumulative distribution functions with nonnegative support. We derive the asymptotic bias and variance of the proposed estimator in both boundary and interior regions and show that it is free
Behzad Mansouri +3 more
doaj +1 more source
On the almost sure convergence of sums [PDF]
Statistics & Probability Letters, 2021 Two counterexamples, addressing questions raised in \cite{AD} and \cite{PZ}, are provided. Both counterexamples are related to chaoses. Let $F_n=Y_n+Z_n$. It may be that $F_n\overset{a.s.}\longrightarrow 0$, $F_n\overset{L_{2+δ}}\longrightarrow 0$ and $E\bigl\{\sup_n\,\abs{F_n}^δ\bigr\}0$ and $Y_n$ and $Z_n$ belong to chaoses of uniformly bounded ...
Pratelli Luca, Rigo Pietro
openaire +4 more sources
Results in Control and Optimization, 2023 In this paper, split step theta balanced Euler approximations for stochastic time-varying delay Hopfield neural networks (HNN) with distributed delays are examined for their exponential stability and strong convergence.
Pichamuthu Mayavel +1 more
doaj +1 more source
Several Different Types of Convergence for ND Random Variables under Sublinear Expectations
Discrete Dynamics in Nature and Society, 2021 The goal of this paper is to build average convergence and almost sure convergence for ND (negatively dependent) sequences of random variables under sublinear expectation space.
Ziwei Liang, Qunying Wu
doaj +1 more source
IET Control Theory & Applications, 2021 Stochastic gradient descent algorithm is a classical and useful method for stochastic optimisation. While stochastic gradient descent has been theoretically investigated for decades and successfully applied in machine learning such as training of deep ...
Xiaoxue Geng, Gao Huang, Wenxiao Zhao
doaj +1 more source
Convergence and Stability of Modified Random SP-Iteration for A Generalized Asymptotically Quasi-Nonexpansive Mappings [PDF]
Mathematics Interdisciplinary Research, 2017 The purpose of this paper is to study the convergence and the almost sure T-stability of the modified SP-type random iterative algorithm in a separable Banach spaces.
Rashwan, Hasanen Hammad
doaj +1 more source
Almost Sure Convergence for the Maximum and Minimum of Normal Vector Sequences
Mathematics, 2020 In this paper, we prove the almost sure convergences for the maximum and minimum of nonstationary and stationary standardized normal vector sequences under some suitable conditions.
Zhicheng Chen +2 more
doaj +1 more source
Necessary and Sufficient Conditions for Stochastic Convergence of the Kernel Estimation of the Intensity Function of Non-Homogeneous Poisson Process in R² [PDF]
The Egyptian Statistical Journal, 2002 The intensity function of the non-homogeneous Poisson process, that is defined on R² will be estimated by using kernel method, and it will be searched for necessary and sufficient conditions to have a uniform convergence in probability, almost sure, and ...
Zakia Kalantan +2 more
doaj +1 more source