Complete f -moment convergence for sums of asymptotically almost negatively associated random variables with statistical applications

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2023-10-04 DOI:10.1080/17442508.2023.2263606

Houlin Zhou, Chao Lu, Xuejun Wang

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Abstract

AbstractIn this paper, we mainly study the complete f-moment convergence for sums of asymptotically almost negatively associated (AANA, for short) random variables and provide an application. A general result on complete f-moment convergence for arrays of rowwise AANA random variables is obtained. We also give an application to nonparametric regression models based on AANA errors by using the result on complete f-moment convergence that we have established. A sufficient and necessary moment condition for the complete consistency is presented. Finally, a numerical simulation is provided to verify the validity of the theoretical result.Keywords: Asymptotically almost negatively associated random variablescomplete f-moment convergencecomplete convergencenonparametric regression modelcomplete consistencyMathematical subject classifications: 60F1562G05 AcknowledgmentsThe authors are most grateful to the Editor and anonymous referee for carefully reading the manuscript and valuable suggestions which helped in improving an earlier version of this paper.Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingSupported by the National Social Science Foundation of China (22BTJ059).

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渐近几乎负相关随机变量和的完全f矩收敛与统计应用

摘要本文主要研究渐近几乎负相关(AANA)随机变量和的完全f矩收敛性，并给出了一个应用。得到了行AANA随机变量阵列完全f矩收敛的一般结果。利用所建立的完全f矩收敛的结果，给出了基于AANA误差的非参数回归模型的一个应用。给出了完全一致性的充分必要矩条件。最后，通过数值仿真验证了理论结果的有效性。关键词:渐近几乎负相关随机变量完全f矩收敛完全收敛非参数回归模型完全一致性数学主题分类:60F1562G05致谢作者非常感谢编辑和匿名审稿人仔细阅读稿件并提出宝贵意见，帮助改进本文的早期版本。披露声明作者未报告潜在的利益冲突。附加信息国家社会科学基金项目(22BTJ059)资助。

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来源期刊

Stochastics-An International Journal of Probability and Stochastic Processes MATHEMATICS, APPLIED-STATISTICS & PROBABILITY

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Stochastics: An International Journal of Probability and Stochastic Processes is a world-leading journal publishing research concerned with stochastic processes and their applications in the modelling, analysis and optimization of stochastic systems, i.e. processes characterized both by temporal or spatial evolution and by the presence of random effects. Articles are published dealing with all aspects of stochastic systems analysis, characterization problems, stochastic modelling and identification, optimization, filtering and control and with related questions in the theory of stochastic processes. The journal also solicits papers dealing with significant applications of stochastic process theory to problems in engineering systems, the physical and life sciences, economics and other areas. Proposals for special issues in cutting-edge areas are welcome and should be directed to the Editor-in-Chief who will review accordingly. In recent years there has been a growing interaction between current research in probability theory and problems in stochastic systems. The objective of Stochastics is to encourage this trend, promoting an awareness of the latest theoretical developments on the one hand and of mathematical problems arising in applications on the other.