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
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
In this paper, we investigate the complete moment convergence for dependent linear processes with random coefficients to form Xt =∑j^∞=∞ Aj∈t-j,where {∈n, n ∈ Z} is a sequence of END stochastically dominated ran...In this paper, we investigate the complete moment convergence for dependent linear processes with random coefficients to form Xt =∑j^∞=∞ Aj∈t-j,where {∈n, n ∈ Z} is a sequence of END stochastically dominated random variables and {An,n ∈ Z} is a sequence of random varibles. As applications, the convergence rate, Marcinkiewicz-Zvgmund strong law and strong law of large numbers for this linear process are established.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
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, 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 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
In this paper,an exponential inequality for weighted sums of identically distributed NOD （negatively orthant dependent） random variables is established,by which we obtain the almost sure convergence rate of which re...In this paper,an exponential inequality for weighted sums of identically distributed NOD （negatively orthant dependent） random variables is established,by which we obtain the almost sure convergence rate of which reaches the available one for independent random variables in terms of Berstein type inequality. As application,we obtain the relevant exponential inequality for Priestley-Chao estimator of nonparametric regression estimate under NOD samples,from which the strong consistency rate is also obtained.展开更多
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.
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.
文摘In this paper, we investigate the complete moment convergence for dependent linear processes with random coefficients to form Xt =∑j^∞=∞ Aj∈t-j,where {∈n, n ∈ Z} is a sequence of END stochastically dominated random variables and {An,n ∈ Z} is a sequence of random varibles. As applications, the convergence rate, Marcinkiewicz-Zvgmund strong law and strong law of large numbers for this linear process are established.
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 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 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Supported by the National Natural Science Foundation of China ( 11061007)
文摘In this paper,an exponential inequality for weighted sums of identically distributed NOD （negatively orthant dependent） random variables is established,by which we obtain the almost sure convergence rate of which reaches the available one for independent random variables in terms of Berstein type inequality. As application,we obtain the relevant exponential inequality for Priestley-Chao estimator of nonparametric regression estimate under NOD samples,from which the strong consistency rate is also obtained.
