In this paper, an exponential inequality for the maximal partial sums of negatively superadditive-dependent （NSD, in short） random variables is established. By uSing the exponen- tial inequality, we present some gen...In this paper, an exponential inequality for the maximal partial sums of negatively superadditive-dependent （NSD, in short） random variables is established. By uSing the exponen- tial inequality, we present some general results on the complete convergence for arrays of rowwise NSD random variables, which improve or generalize the corresponding ones of Wang et al. [28] and Chen et al. [2]. In addition, some sufficient conditions to prove the complete convergence are provided. As an application of the complete convergence that we established, we further investigate the complete consistency and convergence rate of the estimator in a nonparametric regression model based on NSD errors.展开更多
In the paper, the complete convergence for the maximum of weighted sums of negatively superadditive dependent(NSD, in short) random variables is investigated by using the Rosenthal type inequality. Some sufficient con...In the paper, the complete convergence for the maximum of weighted sums of negatively superadditive dependent(NSD, in short) random variables is investigated by using the Rosenthal type inequality. Some sufficient conditions are presented to prove the complete convergence. The result obtained in the paper generalizes some corresponding ones for independent random variables and negatively associated random variables.展开更多
In the paper, the strong convergence properties for two different weighted sums of negatively orthant dependent(NOD) random variables are investigated. Let {X, n ≥ 1}be a sequence of NOD random variables. The results...In the paper, the strong convergence properties for two different weighted sums of negatively orthant dependent(NOD) random variables are investigated. Let {X, n ≥ 1}be a sequence of NOD random variables. The results obtained in the paper generalize the corresponding ones for i.i.d. random variables and identically distributed NA random variables to the case of NOD random variables, which are stochastically dominated by a random variable X. As a byproduct, the Marcinkiewicz-Zygmund type strong law of large numbers for NOD random variables is also obtained.展开更多
A general result on the strong convergence rate and complete convergence for arrays of rowwise extended negatively dependent random variables is established. As applications, some well-known results on negatively depe...A general result on the strong convergence rate and complete convergence for arrays of rowwise extended negatively dependent random variables is established. As applications, some well-known results on negatively dependent random variables can be easily extended to the case of arrays of rowwise extended negatively dependent random variables.展开更多
By using Rosenthal type moment inequality for extended negatively de- pendent random variables, we establish the equivalent conditions of complete convergence for weighted sums of sequences of extended negatively depe...By using Rosenthal type moment inequality for extended negatively de- pendent random variables, we establish the equivalent conditions of complete convergence for weighted sums of sequences of extended negatively dependent random variables under more general conditions. These results complement and improve the corresponding results obtained by Li et al. （Li D L, RAO M B, Jiang T F, Wang X C. Complete convergence and almost sure convergence of weighted sums of random variables. J. Theoret. Probab., 1995, 8： 49-76） and Liang （Liang H Y. Complete convergence for weighted sums of negatively associated random variables. Statist. Probab. Lett., 2000, 48： 317-325）.展开更多
In this paper, we obtain the strong law of large numbers for a 2-dimensional array of pairwise negatively dependent random variables which are not required to be identically distributed. We found the sufficient condit...In this paper, we obtain the strong law of large numbers for a 2-dimensional array of pairwise negatively dependent random variables which are not required to be identically distributed. We found the sufficient conditions of strong law of large numbers for the difference of random variables which independent and identically distributed conditions are regarded. In this study, we consider the limit as which is stronger than the limit as m× n→?∞ when m, n →?∞?are natural numbers.展开更多
Let {X_(nk), k ≥ 1, n ≥ 1} be an array of rowwise negatively superadditive dependent random variables and {a_n, n ≥ 1} be a sequence of positive real numbers such that a_n↑∞. Under some suitable conditions,L_r co...Let {X_(nk), k ≥ 1, n ≥ 1} be an array of rowwise negatively superadditive dependent random variables and {a_n, n ≥ 1} be a sequence of positive real numbers such that a_n↑∞. Under some suitable conditions,L_r convergence of 1/an max 1≤j≤n |j∑k=1 X_(nk)| is studied. The results obtained in this paper generalize and improve some corresponding ones for negatively associated random variables and independent random variables.展开更多
In this paper, the complete convergence is established for the weighted sums of negatively superadditive-dependent random variables. As an application, the Marcinkiewicz-Zygmund strong law of large numbers for the ran...In this paper, the complete convergence is established for the weighted sums of negatively superadditive-dependent random variables. As an application, the Marcinkiewicz-Zygmund strong law of large numbers for the random weighted average is also achieved, and a simulation study is done for the asymptotic behaviour of random weighting estimator.展开更多
In this paper, by using some inequalities of negatively orthant dependent(NOD,in short) random variables and the truncated method of random variables, we investigate the nonparametric regression model. The complete co...In this paper, by using some inequalities of negatively orthant dependent(NOD,in short) random variables and the truncated method of random variables, we investigate the nonparametric regression model. The complete consistency result for the estimator of g(x) is presented.展开更多
In the paper,we establish some exponential inequalities for non-identically distributed negatively orthant dependent(NOD,for short)random variables.In addition,we also establish some exponential inequalities for the p...In the paper,we establish some exponential inequalities for non-identically distributed negatively orthant dependent(NOD,for short)random variables.In addition,we also establish some exponential inequalities for the partial sum and the maximal partial sum of identically distributed NOD random variables.As an application,the Kolmogorov strong law of large numbers for identically distributed NOD random variables is obtained.Our results partially generalize or improve some known results.展开更多
In this paper, we establish a complete convergence result and a complete moment convergence result for weighted sums of widely orthant dependent random variables under mild conditions. As corollaries, the correspondin...In this paper, we establish a complete convergence result and a complete moment convergence result for weighted sums of widely orthant dependent random variables under mild conditions. As corollaries, the corresponding results for weighted sums of extended negatively orthant dependent random variables are also obtained, which generalize and improve the related known works in the literature.展开更多
We give the conditionally residual h-integrability with exponent r for an array of random variables and establish the conditional mean convergence of conditionally negatively quadrant dependent and conditionally negat...We give the conditionally residual h-integrability with exponent r for an array of random variables and establish the conditional mean convergence of conditionally negatively quadrant dependent and conditionally negative associated random variables under this integrability. These results generalize and improve the known ones.展开更多
In this paper,the complete convergence and the complete moment convergence for extended negatively dependent(END,in short) random variables without identical distribution are investigated.Under some suitable condition...In this paper,the complete convergence and the complete moment convergence for extended negatively dependent(END,in short) random variables without identical distribution are investigated.Under some suitable conditions,the equivalence between the moment of random variables and the complete convergence is established.In addition,the equivalence between the moment of random variables and the complete moment convergence is also proved.As applications,the Marcinkiewicz-Zygmund-type strong law of large numbers and the Baum-Katz-type result for END random variables are established.The results obtained in this paper extend the corresponding ones for independent random variables and some dependent random variables.展开更多
基金Supported by the National Natural Science Foundation of China(11501004,11501005,11526033,11671012)the Natural Science Foundation of Anhui Province(1508085J06,1608085QA02)+1 种基金the Key Projects for Academic Talent of Anhui Province(gxbj ZD2016005)the Research Teaching Model Curriculum of Anhui University(xjyjkc1407)
文摘In this paper, an exponential inequality for the maximal partial sums of negatively superadditive-dependent （NSD, in short） random variables is established. By uSing the exponen- tial inequality, we present some general results on the complete convergence for arrays of rowwise NSD random variables, which improve or generalize the corresponding ones of Wang et al. [28] and Chen et al. [2]. In addition, some sufficient conditions to prove the complete convergence are provided. As an application of the complete convergence that we established, we further investigate the complete consistency and convergence rate of the estimator in a nonparametric regression model based on NSD errors.
基金Supported by the Natural Science Foundation of Anhui Province(1508085J06)Supported by the Research Teaching Model Curriculum of Anhui University(xjyjkc1407)Supported by the Students Innovative Training Project of Anhui University(201510357118)
文摘In the paper, the complete convergence for the maximum of weighted sums of negatively superadditive dependent(NSD, in short) random variables is investigated by using the Rosenthal type inequality. Some sufficient conditions are presented to prove the complete convergence. The result obtained in the paper generalizes some corresponding ones for independent random variables and negatively associated random variables.
基金Supported by the National Natural Science Foundation of China(11671012,11501004,11501005)the Natural Science Foundation of Anhui Province(1508085J06)+2 种基金the Key Projects for Academic Talent of Anhui Province(gxbj ZD2016005)the Quality Engineering Project of Anhui Province(2016jyxm0047)the Graduate Academic Innovation Research Project of Anhui University(yfc100004)
文摘In the paper, the strong convergence properties for two different weighted sums of negatively orthant dependent(NOD) random variables are investigated. Let {X, n ≥ 1}be a sequence of NOD random variables. The results obtained in the paper generalize the corresponding ones for i.i.d. random variables and identically distributed NA random variables to the case of NOD random variables, which are stochastically dominated by a random variable X. As a byproduct, the Marcinkiewicz-Zygmund type strong law of large numbers for NOD random variables is also obtained.
基金Supported by the National Natural Science Foundation of China（11201001） Supported by the Natural Science Foundation of Anhui Province（1208085QA03, 1308085QA03）+1 种基金 Supported by the Research Teaching Model Curriculum of Anhui University（xjyjkc1407） Supported by the Students Science Research Training Program of Anhui University（KYXL2014017）
Acknowledgement The authors are most grateful to the editor and anonymous referees for careful reading of the manuscript and valuable suggestions which helped in significantly improving an earlier version of this paper.
文摘A general result on the strong convergence rate and complete convergence for arrays of rowwise extended negatively dependent random variables is established. As applications, some well-known results on negatively dependent random variables can be easily extended to the case of arrays of rowwise extended negatively dependent random variables.
基金The NSF(11271020 and 11201004)of Chinathe NSF(10040606Q30 and 1208085MA11)of Anhui Provincethe NSF(KJ2012ZD01)of Education Department of Anhui Province
文摘By using Rosenthal type moment inequality for extended negatively de- pendent random variables, we establish the equivalent conditions of complete convergence for weighted sums of sequences of extended negatively dependent random variables under more general conditions. These results complement and improve the corresponding results obtained by Li et al. （Li D L, RAO M B, Jiang T F, Wang X C. Complete convergence and almost sure convergence of weighted sums of random variables. J. Theoret. Probab., 1995, 8： 49-76） and Liang （Liang H Y. Complete convergence for weighted sums of negatively associated random variables. Statist. Probab. Lett., 2000, 48： 317-325）.
文摘In this paper, we obtain the strong law of large numbers for a 2-dimensional array of pairwise negatively dependent random variables which are not required to be identically distributed. We found the sufficient conditions of strong law of large numbers for the difference of random variables which independent and identically distributed conditions are regarded. In this study, we consider the limit as which is stronger than the limit as m× n→?∞ when m, n →?∞?are natural numbers.
基金Supported by the Provincial Natural Science Research Project of Anhui Colleges(KJ2015A018)Supported by the Students Science Research Training Program of Anhui University(kyxl2013003)+2 种基金Supported by the Students Innovative Training Project of Anhui University(201410357118)Supported by the Quality Engineering Project of Anhui Province(2015jyxm045)Supported by the Quality Improvement Project for Undergraduate Education of Anhui University(ZLTS2015035)
文摘Let {X_(nk), k ≥ 1, n ≥ 1} be an array of rowwise negatively superadditive dependent random variables and {a_n, n ≥ 1} be a sequence of positive real numbers such that a_n↑∞. Under some suitable conditions,L_r convergence of 1/an max 1≤j≤n |j∑k=1 X_(nk)| is studied. The results obtained in this paper generalize and improve some corresponding ones for negatively associated random variables and independent random variables.
基金supported by a grant from Ferdowsi University of Mashhad(NO.2/42843)
文摘In this paper, the complete convergence is established for the weighted sums of negatively superadditive-dependent random variables. As an application, the Marcinkiewicz-Zygmund strong law of large numbers for the random weighted average is also achieved, and a simulation study is done for the asymptotic behaviour of random weighting estimator.
基金Supported by the Research Teaching Model Curriculum of Anhui University(xjyjkc1407)Supported by the Students Innovative Training Project of Anhui University(201310357004,201410357117,201410357249)Supported by the Quality Improvement Projects for Undergraduate Education of Anhui University(ZLTS2015035)
文摘In this paper, by using some inequalities of negatively orthant dependent(NOD,in short) random variables and the truncated method of random variables, we investigate the nonparametric regression model. The complete consistency result for the estimator of g(x) is presented.
基金This paper is supported by the National Natural Science Foundation of China(Nos.11671012,11871072,11701004,11701005)the Natural Science Foundation of Anhui Province(Nos.1808085QA03,1908085QA01,1908085QA07)and the Provincial Natural Science Research Project of Anhui Colleges(KJ2019A0001,KJ2019A0003).
文摘In the paper,we establish some exponential inequalities for non-identically distributed negatively orthant dependent(NOD,for short)random variables.In addition,we also establish some exponential inequalities for the partial sum and the maximal partial sum of identically distributed NOD random variables.As an application,the Kolmogorov strong law of large numbers for identically distributed NOD random variables is obtained.Our results partially generalize or improve some known results.
基金Supported by National Natural Science Foundation of China(Grant No.11271161)
文摘In this paper, we establish a complete convergence result and a complete moment convergence result for weighted sums of widely orthant dependent random variables under mild conditions. As corollaries, the corresponding results for weighted sums of extended negatively orthant dependent random variables are also obtained, which generalize and improve the related known works in the literature.
基金Acknowledgements The authors thank Editor Lu and two anonymous referees for their constructive suggestions and comments which helped in significantly improving an earlier version of this paper. This work is supported by the National Natural Science Foundation of China （11171001, 11201001, 11426032）, the Natural Science Foundation of Anhui Province （1308085QA03, 1408085QA02）, the Science Fund for Distinguished Young Scholars of Anhui Province （1508085J06）, and Introduction Projects of Anhui University Academic and Technology Leaders.
文摘We give the conditionally residual h-integrability with exponent r for an array of random variables and establish the conditional mean convergence of conditionally negatively quadrant dependent and conditionally negative associated random variables under this integrability. These results generalize and improve the known ones.
基金supported by the National Natural Science Foundation of China(Nos.11501004,11501005,11526033)the Natural Science Foundation of Anhui Province(No.1508085J06)+4 种基金the Key Projects for Academic Talent of Anhui Province(No.gxbj ZD2016005)the Provincial Natural Science Research Project of Anhui Colleges(No.KJ2015A018)the Open Project of School of Mathematical Sciences,Anhui University(No.ADSY201503)the Quality Engineering Project of Anhui Province(No.2015jyxm045)the Quality Improvement Projects for Undergraduate Education of Anhui University(No.ZLTS2015035)
文摘In this paper,the complete convergence and the complete moment convergence for extended negatively dependent(END,in short) random variables without identical distribution are investigated.Under some suitable conditions,the equivalence between the moment of random variables and the complete convergence is established.In addition,the equivalence between the moment of random variables and the complete moment convergence is also proved.As applications,the Marcinkiewicz-Zygmund-type strong law of large numbers and the Baum-Katz-type result for END random variables are established.The results obtained in this paper extend the corresponding ones for independent random variables and some dependent random variables.
