Esaim-Probability and Statistics最新文献_第10页

The probabilities of large deviations for a certain class of statistics associated with multinomial distribution 与多项分布有关的某一类统计量的大偏差的概率

IF 0.4 4区数学

Esaim-Probability and Statistics Pub Date : 2020-01-01 DOI: 10.1051/ps/2020020

S. Mirakhmedov

引用次数: 3

On Bernstein–Kantorovich invariance principle in Hölder spaces and weighted scan statistics Hölder空间中的Bernstein-Kantorovich不变性原理与加权扫描统计量

IF 0.4 4区数学

Esaim-Probability and Statistics Pub Date : 2020-01-01 DOI: 10.1051/ps/2019027

A. Račkauskas, Charles Suquet

{"title":"On Bernstein–Kantorovich invariance principle in Hölder spaces and weighted scan statistics","authors":"A. Račkauskas, Charles Suquet","doi":"10.1051/ps/2019027","DOIUrl":"https://doi.org/10.1051/ps/2019027","url":null,"abstract":"Let ξn be the polygonal line partial sums process built on i.i.d. centered random variables Xi, i ≥ 1. The Bernstein-Kantorovich theorem states the equivalence between the finiteness of E|X1|max(2,r) and the joint weak convergence in C[0, 1] of n−1∕2ξn to a Brownian motion W with the moments convergence of E∥n−1/2ξn∥∞r to E∥W∥∞r. For 0 < α < 1∕2 and p (α) = (1 ∕ 2 - α) -1, we prove that the joint convergence in the separable Hölder space Hαo of n−1∕2ξn to W jointly with the one of E∥n−1∕2ξn∥αr to E∥W∥αr holds if and only if P(|X1| > t) = o(t−p(α)) when r < p(α) or E|X1|r < ∞ when r ≥ p(α). As an application we show that for every α < 1∕2, all the α-Hölderian moments of the polygonal uniform quantile process converge to the corresponding ones of a Brownian bridge. We also obtain the asymptotic behavior of the rth moments of some α-Hölderian weighted scan statistics where the natural border for α is 1∕2 − 1∕p when E|X1|p < ∞. In the case where the Xi’s are p regularly varying, we can complete these results for α > 1∕2 − 1∕p with an appropriate normalization.","PeriodicalId":51249,"journal":{"name":"Esaim-Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90288193","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4

Continuous-time Markov processes, orthogonal polynomials and Lancaster probabilities 连续时间马尔可夫过程，正交多项式和兰开斯特概率

IF 0.4 4区数学

Esaim-Probability and Statistics Pub Date : 2020-01-01 DOI: 10.1051/ps/2020004

R. H. Mena, Freddy Palma

引用次数: 1

A probabilistic approach to quasilinear parabolic PDEs with obstacle and Neumann problems 带障碍和Neumann问题的拟线性抛物型偏微分方程的概率方法

IF 0.4 4区数学

Esaim-Probability and Statistics Pub Date : 2020-01-01 DOI: 10.1051/ps/2019023

Lishun Xiao, Shengjun Fan, D. Tian

引用次数: 1

The Berry-Esseen bound of a wavelet estimator in non-randomly designed nonparametric regression model based on ANA errors 基于ANA误差的非随机设计非参数回归模型中小波估计量的Berry-Esseen界

IF 0.4 4区数学

Esaim-Probability and Statistics Pub Date : 2020-01-01 DOI: 10.1051/PS/2019017

Xu-fei Tang, Xuejun Wang, Yi Wu, Fei Zhang

引用次数: 1

The logarithmic Zipf law in a general urn problem 一般瓮问题的对数齐夫律

IF 0.4 4区数学

Esaim-Probability and Statistics Pub Date : 2020-01-01 DOI: 10.1051/ps/2020011

Aristides V. Doumas, V. Papanicolaou

{"title":"The logarithmic Zipf law in a general urn problem","authors":"Aristides V. Doumas, V. Papanicolaou","doi":"10.1051/ps/2020011","DOIUrl":"https://doi.org/10.1051/ps/2020011","url":null,"abstract":"The origin of power-law behavior (also known variously as Zipf’s law) has been a topic of debate in the scientific community for more than a century. Power laws appear widely in physics, biology, earth and planetary sciences, economics and finance, computer science, demography and the social sciences. In a highly cited article, Mark Newman [Contemp. Phys. 46 (2005) 323–351] reviewed some of the empirical evidence for the existence of power-law forms, however underscored that even though many distributions do not follow a power law, quite often many of the quantities that scientists measure are close to a Zipf law, and hence are of importance. In this paper we engage a variant of Zipf’s law with a general urn problem. A collector wishes to collect m complete sets of N distinct coupons. The draws from the population are considered to be independent and identically distributed with replacement, and the probability that a type-j coupon is drawn is denoted by p j , j = 1, 2, …, N . Let T m (N ) the number of trials needed for this problem. We present the asymptotics for the expectation (five terms plus an error), the second rising moment (six terms plus an error), and the variance of T m (N ) (leading term) as N →∞ , when p j = a j / ∑j =2 N +1 a j , where a j = (ln j )−p , p > 0. begin{equation*} p_{j}=frac{a_{j}}{sum_{j=2}^{N+1} a_{j}}, ,,,text{where},,, a_{j}=left(ln jright)^{-p}, ,,p>0.end{equation*} pj=aj ∑ j=2N+1aj,whereaj= lnj-p,p>0. Moreover, we prove that T m (N ) (appropriately normalized) converges in distribution to a Gumbel random variable. These “log-Zipf” classes of coupon probabilities are not covered by the existing literature and the present paper comes to fill this gap. In the spirit of a recent paper of ours [ESAIM: PS 20 (2016) 367–399] we enlarge the classes for which the Dixie cup problem is solved w.r.t. its moments, variance, distribution.","PeriodicalId":51249,"journal":{"name":"Esaim-Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73591282","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

Exit-time of mean-field particles system 平均场粒子系统的退出时间

IF 0.4 4区数学

Esaim-Probability and Statistics Pub Date : 2020-01-01 DOI: 10.1051/ps/2019028

J. Tugaut

引用次数: 2

Approximation of the invariant distribution for a class of ergodic jump diffusions 一类遍历跳跃扩散的不变分布的近似

IF 0.4 4区数学

Esaim-Probability and Statistics Pub Date : 2020-01-01 DOI: 10.1051/PS/2020023

A. Gloter, Igor Honoré, D. Loukianova

引用次数: 3

One-step estimation for the fractional Gaussian noise at high-frequency 高频分数阶高斯噪声的一步估计

IF 0.4 4区数学

Esaim-Probability and Statistics Pub Date : 2020-01-01 DOI: 10.1051/PS/2020022

A. Brouste, M. Soltane, I. Votsi

引用次数: 6

Random forests for time-dependent processes 时间相关过程的随机森林

IF 0.4 4区数学

Esaim-Probability and Statistics Pub Date : 2020-01-01 DOI: 10.1051/PS/2020015

Benjamin Goehry

引用次数: 16