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Strong Law of Large Numbers for weighted sums of Random Variables and Its Applications in EV Regression Models

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Journal of Systems Science & Complexity 2022年第1期35卷 342-360页

作者： PENG Yunjie ZHENG Xiaoqian YU Wei HE Kaixin WANG Xuejun School of Mathematical Sciences Anhui UniversityHefei 230601China. Wendian College Anhui UniversityHefei 230601China

This paper mainly studies the strong convergence properties for weighted sums of extended negatively dependent(END,for short)random *** sufficient conditions to prove the strong law of large numbers for weighted sums of END random variables are *** particular,the authors obtain the weighted version of Kolmogorov type strong law of large numbers for END random variables as a *** results that the authors obtained generalize the corresponding ones for independent random variables and some dependent random *** an application,the authors investigate the errors-in-variables(EV,for short)regression models and establish the strong consistency for the least square *** studies are conducted to demonstrate the performance of the proposed procedure and a real example is analysed for illustration.

关键词： EV regression models extended negatively dependent random variables strong consistency strong law of large numbers weighted sums

ON ALMOST SURE CONVERGENCE OF weighted sums OF RANDOM ELEMENT SEQUENCES

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Acta Mathematica Scientia 2010年第4期30卷 1021-1028页

作者：甘师信 School of Mathematics and Statistics Wuhan University

We mainly study the almost sure limiting behavior of weighted sums of the form ∑ni=1 aiXi/bn , where {Xn, n ≥ 1} is an arbitrary Banach space valued random element sequence or Banach space valued martingale difference sequence and {an, n ≥ 1} and {bn,n ≥ 1} are two sequences of positive constants. Some new strong laws of large numbers for such weighted sums are proved under mild conditions.

关键词： Strong law of large number almost sure convergence Lp convergence weighted sums Banach space valued random element sequence Banach space martingale difference sequence

Complete Convergence of weighted sums for ρ*-Mixing Sequence of Random Variables

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Journal of Mathematical Research with Applications 2013年第4期33卷 483-492页

作者： Mingle GUO Dongjin ZHU School of Mathematics and Computer Science Anhui Normal University

In this paper, the complete convergence of weighted sums for ρ*-mixing sequence of random variables is investigated. By applying moment inequality and truncation methods, the equivalent conditions of complete convergence of weighted sums for ρ*-mixing sequence of random variables are established. We not only promote and improve the results of Li et al. (J. Theoret. Probab., 1995, 8(1): 49-76) from i.i.d. to ρ*-mixing setting but also obtain their necessities and relax their conditions.

关键词： ρ*-mixing sequence of random variables weighted sums complete convergence moment inequality.

Strong Limit Theorems for weighted sums of Widely Orthant Dependent Random Variables

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Journal of Mathematical Research with Applications 2014年第1期34卷 105-113页

作者： Dehua QIU Tienchung HU School of Mathematics and Statistics Guangdong University of Finance and Economics Department of Mathematics National Tsing Hua University

Strong limit theorems are established for weighted sums of widely orthant dependent(WOD)random *** corollaries,the strong limit theorems for weighted sums of extended negatively orthant dependent(ENOD)random variables... 详细信息

关键词： widely orthant dependent(WOD) random variables extended negatively orthant dependent(ENOD) random variables weighted sums strong limit theorem.

Complete Conyergence and Strong Laws of Large Numbers-for weighted sums of Sequences of Independent B-Valued Random Elements

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Journal of Mathematical Research and Exposition 2009年第3期29卷 528-534页

作者： QIU De Hua Department of Mathematics Guangdong University of Business Studies Guangdong 510320 China

In this paper, we obtain theorems of complete convergence and strong laws of large numbers for weighted sums of sequences of independent random elements in a Banach space of type p （1 ≤ p ≤ 2）. The results improve... 详细信息

关键词： B-valued random elements weighted sums complete convergence strong laws oflarge numbers space of type p

Complete Convergence for weighted sums of Arrays of Rowwise Negatively Associated Random Variables

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Journal of Mathematical Research and Exposition 2010年第1期30卷 149-158页

作者： De Hua QIU School of Mathematics and Computational Science Guangdong University of Business Studies Guangdong 510320 P. R. China

In this paper we obtain theorems of complete convergence for weighted sums of arrays of rowwise negatively associated （NA） random variables. These results improve and extend the corresponding results obtained by Su... 详细信息

关键词： complete convergence negatively associated random variable weighted sums slowly varying function.

Complete Convergence for weighted sums of φ-mixing Sequence

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Chinese Quarterly Journal of Mathematics 2017年第2期32卷 161-171页

作者： LIU Ting-ting WANG Xue-jun WANG Xing-hui Department of Finance and Economics Hefei Economic and Trade Tourism School Hefei 230011 China Department of Statistics Anhui University Hefei 230601 China

In this paper, the complete convergence and strong law of large numbers for weighted sums of φ-mixing sequence with different distribution are investigated under some weaker moment conditions. Our results extend ones... 详细信息

关键词： weighted sums φ-mixing sequence complete convergence strong law of large numbers

On the Strong Laws for weighted sums of m-negatively Asso ciated Random Variables

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Chinese Quarterly Journal of Mathematics 2014年第2期29卷 265-273页

作者： WU Yong-feng Department of Mathematics and Computer Science Tongling University Tongling 244000 China

In this article, the author establishes the strong laws for linear statistics that are weighted sums of a m-negatively associated(m-NA) random sample. The obtained results extend and improve the result of Qiu and Yang... 详细信息

关键词： Marcinkiewicz-Zygmund strong law complete convergence weighted sums m-negatively associated random variable

Complete Convergence for weighted sums of WOD Random Variables

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Chinese Quarterly Journal of Mathematics 2016年第1期31卷 1-8页

作者： ZHANG Ying ZHANG Yu SHEN Ai-ting School of Mathematical Sciences Anhui University

In this article, we study the complete convergence for weighted sums of widely orthant dependent random variables. By using the exponential probability inequality, we establish a complete convergence result for weighted sums of widely orthant dependent random variables under mild conditions of weights and moments. The result obtained in the paper generalizes the corresponding ones for independent random variables and negatively dependent random variables.

关键词： widely orthant dependence complete convergence weighted sums