Journal of Complexity最新文献

On upper and lower bounds for pathwise approximation of scalar SDEs with reflection 带反射的标量SDEs路径逼近的上界和下界

IF 1.8 2区数学

Journal of Complexity Pub Date : 2025-05-16 DOI: 10.1016/j.jco.2025.101959

Mario Hefter , André Herzwurm , Klaus Ritter

引用次数: 0

Skewness of a randomized quasi-Monte Carlo estimate 随机拟蒙特卡罗估计的偏度

IF 1.8 2区数学

Journal of Complexity Pub Date : 2025-05-05 DOI: 10.1016/j.jco.2025.101956

Zexin Pan, Art B. Owen

{"title":"Skewness of a randomized quasi-Monte Carlo estimate","authors":"Zexin Pan, Art B. Owen","doi":"10.1016/j.jco.2025.101956","DOIUrl":"10.1016/j.jco.2025.101956","url":null,"abstract":"<div><div>Some recent work on confidence intervals for randomized quasi-Monte Carlo (RQMC) sampling found a surprising result: ordinary Student's <em>t</em> 95% confidence intervals based on a modest number of replicates were seen to be very effective and even more reliable than some bootstrap <em>t</em> intervals that were expected to be best. One potential explanation is that those RQMC estimates have small skewness. In this paper we give conditions under which the skewness is <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mi>ϵ</mi></mrow></msup><mo>)</mo></math></span> for any <span><math><mi>ϵ</mi><mo>></mo><mn>0</mn></math></span>, so ‘almost <span><math><mi>O</mi><mo>(</mo><mn>1</mn><mo>)</mo></math></span>’. Under a random generator matrix model, we can improve this rate to <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mo>−</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>+</mo><mi>ϵ</mi></mrow></msup><mo>)</mo></math></span> with very high probability. We also improve some probabilistic bounds on the distribution of the quality parameter <em>t</em> for a digital net in a prime base under random sampling of generator matrices.</div></div>","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"90 ","pages":"Article 101956"},"PeriodicalIF":1.8,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143908058","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 0

Bounds for the sampling discretization error and their applications to the universal sampling discretization 抽样离散误差的界限及其在通用抽样离散中的应用

IF 1.8 2区数学

Journal of Complexity Pub Date : 2025-05-05 DOI: 10.1016/j.jco.2025.101958

E.D. Kosov , V.N. Temlyakov

引用次数: 0

Average case tractability of multivariate approximation with Gevrey type kernels Gevrey型核多元逼近的平均情况可跟踪性

IF 1.8 2区数学

Journal of Complexity Pub Date : 2025-05-05 DOI: 10.1016/j.jco.2025.101957

Wanting Lu , Heping Wang

引用次数: 0

Tractability results for integration in subspaces of the Wiener algebra 维纳代数子空间积分的可溯性结果

IF 1.8 2区数学

Journal of Complexity Pub Date : 2025-04-16 DOI: 10.1016/j.jco.2025.101948

Josef Dick , Takashi Goda , Kosuke Suzuki

引用次数: 0

Takashi Goda is the winner of the 2025 Joseph F. Traub Prize for Achievement in Information-Based Complexity 后田隆史是 2025 年约瑟夫-特劳布信息复杂性成就奖（Joseph F. Traub Prize for Achievement in Information-Based Complexity）的获得者。

IF 1.8 2区数学

Journal of Complexity Pub Date : 2025-04-10 DOI: 10.1016/j.jco.2025.101947

Erich Novak

引用次数: 0

Constructions of normal numbers with infinite digit sets 具有无限位集的正常数的构造

IF 1.8 2区数学

Journal of Complexity Pub Date : 2025-04-04 DOI: 10.1016/j.jco.2025.101945

Aafko Boonstra , Charlene Kalle

引用次数: 0

Multilevel Picard approximations overcome the curse of dimensionality in the numerical approximation of general semilinear PDEs with gradient-dependent nonlinearities 多阶皮卡德近似克服了一般非线性梯度半线性偏微分方程数值逼近的维数问题

IF 1.8 2区数学

Journal of Complexity Pub Date : 2025-04-04 DOI: 10.1016/j.jco.2025.101946

Ariel Neufeld , Tuan Anh Nguyen , Sizhou Wu

{"title":"Multilevel Picard approximations overcome the curse of dimensionality in the numerical approximation of general semilinear PDEs with gradient-dependent nonlinearities","authors":"Ariel Neufeld , Tuan Anh Nguyen , Sizhou Wu","doi":"10.1016/j.jco.2025.101946","DOIUrl":"10.1016/j.jco.2025.101946","url":null,"abstract":"<div><div>Neufeld and Wu (2023) <span><span>[49]</span></span> developed a multilevel Picard (MLP) algorithm which can approximately solve <em>general</em> semilinear parabolic PDEs with gradient-dependent nonlinearities, allowing also for coefficient functions of the corresponding PDE to be non-constant. By introducing a particular stochastic fixed-point equation (SFPE) motivated by the Feynman-Kac representation and the Bismut-Elworthy-Li formula and identifying the first and second component of the unique fixed-point of the SFPE with the unique viscosity solution of the PDE and its gradient, they proved convergence of their algorithm. However, it remained an open question whether the proposed MLP schema in Neufeld and Wu (2023) <span><span>[49]</span></span> does not suffer from the curse of dimensionality. In this paper, we prove that the MLP algorithm in Neufeld and Wu (2023) <span><span>[49]</span></span> indeed can overcome the curse of dimensionality, i.e. that its computational complexity only grows polynomially in the dimension <span><math><mi>d</mi><mo>∈</mo><mi>N</mi></math></span> and the reciprocal of the accuracy <em>ε</em>, under some suitable assumptions on the nonlinear part of the corresponding PDE.</div></div>","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"90 ","pages":"Article 101946"},"PeriodicalIF":1.8,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144070001","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 0

Nonparametric conditional U-statistics on Lie groups with measurement errors 具有测量误差的李群的非参数条件u统计量

IF 1.8 2区数学

Journal of Complexity Pub Date : 2025-03-31 DOI: 10.1016/j.jco.2025.101944

Salim Bouzebda, Nourelhouda Taachouche

{"title":"Nonparametric conditional U-statistics on Lie groups with measurement errors","authors":"Salim Bouzebda, Nourelhouda Taachouche","doi":"10.1016/j.jco.2025.101944","DOIUrl":"10.1016/j.jco.2025.101944","url":null,"abstract":"<div><div>This study presents a comprehensive framework for conditional <em>U</em>-statistics of a general order in the context of Lie group-valued predictors affected by measurement errors. Such situations arise in a variety of modern statistical problems. Our approach is grounded in an abstract harmonic analysis on Lie groups, a setting relatively underexplored in statistical research. In a unified study, we introduce an innovative deconvolution method for conditional <em>U</em>-statistics and investigate its convergence rate and asymptotic distribution for the first time. Furthermore, we explore the application of conditional <em>U</em>-statistics to variables that combine, in a nontrivial way, Euclidean and non-Euclidean elements subject to measurement errors, an area largely uncharted in statistical research. We derive general asymptotic properties, including convergence rates across various modes and the asymptotic distribution. All results are established under fairly general conditions on the underlying models. Additionally, our results are used to derive the asymptotic confidence intervals derived from the asymptotic distribution of the estimator. We also discuss applications of the general approximation results and give new insights into the Kendall rank correlation coefficient and discrimination problems.</div></div>","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"89 ","pages":"Article 101944"},"PeriodicalIF":1.8,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143768448","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Integrability of weak mixed first-order derivatives and convergence rates of scrambled digital nets 弱混合一阶导数的可积性与乱置数字网络的收敛速度

IF 1.8 2区数学

Journal of Complexity Pub Date : 2025-03-04 DOI: 10.1016/j.jco.2025.101935

Yang Liu

引用次数: 0