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 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,we study the complete f-moment convergence for widely orthant dependent(WOD,for short)random variables.A general result on complete f-moment convergence for arrays of rowwise WOD random variables is obta...In this paper,we study the complete f-moment convergence for widely orthant dependent(WOD,for short)random variables.A general result on complete f-moment convergence for arrays of rowwise WOD random variables is obtained.As applications,we present some new results on complete f-moment convergence for WOD random variables.We also give an application to nonparametric regression models based onWOD errors by using the complete convergence that we established.Finally,the choice of the fixed design points and the weight functions for the nearest neighbor estimator are proposed,and a numerical simulation is provided to verify the validity of the theoretical result.展开更多
In this paper, complete moment convergence for widely orthant dependent random vari- ables is investigated under some mild conditions. For arrays of rowwise widely orthant dependent random variables, the main results ...In this paper, complete moment convergence for widely orthant dependent random vari- ables is investigated under some mild conditions. For arrays of rowwise widely orthant dependent random variables, the main results extend recent results on complete convergence to complete moment convergence. These results on complete moment convergence are shown to yield new results on complete integral convergence.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,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
Let fX;Xn;n≥1g be a sequence of identically distributed pairwise negative quadrant dependent(PNQD)random variables and fan;n1g be a sequence of positive constants with an=f(n)and f(θ^k)=f(θ^k-1)for all large posit...Let fX;Xn;n≥1g be a sequence of identically distributed pairwise negative quadrant dependent(PNQD)random variables and fan;n1g be a sequence of positive constants with an=f(n)and f(θ^k)=f(θ^k-1)for all large positive integers k,where 1<θ≤βand f(x)>0(x≥1)is a non-decreasing function on[b;+1)for some b≥1:In this paper,we obtain the strong law of large numbers and complete convergence for the sequence fX;Xn;n≥1g,which are equivalent to the general moment conditionΣ∞n=1P(|X|>an)<1.Our results extend and improve the related known works in Baum and Katz[1],Chen at al.[3],and Sung[14].展开更多
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 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(Grant Nos.11671012,11871072,11701004 and11701005)the Natural Science Foundation of Anhui Province(Grant Nos.1808085QA03,1908085QA01 and1908085QA07)+1 种基金the Provincial Natural Science Research Project of Anhui Colleges(Grant No.KJ2019A0003)the Project on Reserve Candidates for Academic and Technical Leaders of Anhui Province(Grant No.2017H123)
文摘In this paper,we study the complete f-moment convergence for widely orthant dependent(WOD,for short)random variables.A general result on complete f-moment convergence for arrays of rowwise WOD random variables is obtained.As applications,we present some new results on complete f-moment convergence for WOD random variables.We also give an application to nonparametric regression models based onWOD errors by using the complete convergence that we established.Finally,the choice of the fixed design points and the weight functions for the nearest neighbor estimator are proposed,and a numerical simulation is provided to verify the validity of the theoretical result.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11671012,11501004 and 11501005)the Natural Science Foundation of Anhui Province(Grant No.1508085J06)+1 种基金the Key Projects for Academic Talent of Anhui Province(Grant No.gxbjZD2016005)the Research Teaching Model Curriculum of Anhui University(Grant No.xjyjkc1407)
文摘In this paper, complete moment convergence for widely orthant dependent random vari- ables is investigated under some mild conditions. For arrays of rowwise widely orthant dependent random variables, the main results extend recent results on complete convergence to complete moment convergence. These results on complete moment convergence are shown to yield new results on complete integral convergence.
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 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.
基金Supported by the National Natural Science Foundation of China(No.11271161).
文摘Let fX;Xn;n≥1g be a sequence of identically distributed pairwise negative quadrant dependent(PNQD)random variables and fan;n1g be a sequence of positive constants with an=f(n)and f(θ^k)=f(θ^k-1)for all large positive integers k,where 1<θ≤βand f(x)>0(x≥1)is a non-decreasing function on[b;+1)for some b≥1:In this paper,we obtain the strong law of large numbers and complete convergence for the sequence fX;Xn;n≥1g,which are equivalent to the general moment conditionΣ∞n=1P(|X|>an)<1.Our results extend and improve the related known works in Baum and Katz[1],Chen at al.[3],and Sung[14].
