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
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, the complete convergence and complete moment convergence for maximal weighted sums of extended negatively dependent random variables are investigated. Some sufficient conditions for the convergence are ...In this paper, the complete convergence and complete moment convergence for maximal weighted sums of extended negatively dependent random variables are investigated. Some sufficient conditions for the convergence are provided. In addition, the Marcinkiewicz Zygmund type strong law of large numbers for weighted sums of extended negatively dependent random variables is obtained. The results obtained in the article extend the corresponding ones for independent random variables and some dependent random variables.展开更多
Some exponential inequalities and complete convergence are established for extended negatively dependent(END) random variables. The inequalities extend and improve the results of Kim and Kim(On the exponential inequal...Some exponential inequalities and complete convergence are established for extended negatively dependent(END) random variables. The inequalities extend and improve the results of Kim and Kim(On the exponential inequality for negative dependent sequence.Communications of the Korean Mathematical Society, 2007, 22(2): 315-321) and Nooghabi and Azarnoosh(Exponential inequality for negatively associated random variables. Statistical Papers, 2009, 50(2): 419-428). We also obtain the convergence rate O(n-1/2ln1/2n) for the strong law of large numbers, which improves the corresponding ones of Kim and Kim,and Nooghabi and Azarnoosh.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
We establish some strong limit theorems for a sequence of pair-wise extended lower/upper negatively dependent random variables and give some new examples of dependent random variables.
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
Some probability inequalities are established for extended negatively dependent(END) random variables. The inequalities extend some corresponding ones for negatively associated random variables and negatively orthant ...Some probability inequalities are established for extended negatively dependent(END) random variables. The inequalities extend some corresponding ones for negatively associated random variables and negatively orthant dependent random variables. By using these probability inequalities, we further study the complete convergence for END random variables. We also obtain the convergence rate O(n-1/2ln1/2n) for the strong law of large numbers, which generalizes and improves the corresponding ones for some known results.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 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 the paper,we get the precise results of Hájek-Rényi type inequalities for the partial sums of negatively orthant dependent sequences,which improve the results of Theorem 3.1and Corollary 3.2 in Kim(2006)a...In the paper,we get the precise results of Hájek-Rényi type inequalities for the partial sums of negatively orthant dependent sequences,which improve the results of Theorem 3.1and Corollary 3.2 in Kim(2006)and the strong law of large numbers and strong growth rate for negatively orthant dependent sequences.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
This paper establishes some asymptotic formulas for the infinite-time ruin probabilities of two kinds of dependent risk models. One risk model considers the claim sizes as a modulated process, and the other deals with...This paper establishes some asymptotic formulas for the infinite-time ruin probabilities of two kinds of dependent risk models. One risk model considers the claim sizes as a modulated process, and the other deals with negatively upper orthant dependent claim sizes. In the two models, the inter-arrival times are both assumed to be negatively lower orthant dependent.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
This paper mainly studies the strong convergence properties for weighted sums of extended negatively dependent(END,for short)random variables.Some sufficient conditions to prove the strong law of large numbers for wei...This paper mainly studies the strong convergence properties for weighted sums of extended negatively dependent(END,for short)random variables.Some sufficient conditions to prove the strong law of large numbers for weighted sums of END random variables are provided.In particular,the authors obtain the weighted version of Kolmogorov type strong law of large numbers for END random variables as a product.The results that the authors obtained generalize the corresponding ones for independent random variables and some dependent random variables.As an application,the authors investigate the errors-in-variables(EV,for short)regression models and establish the strong consistency for the least square estimators.Simulation studies are conducted to demonstrate the performance of the proposed procedure and a real example is analysed for illustration.展开更多
In 2007,Chen and Ng investigated infinite-time ruin probability with constant interest forceand negatively quadrant dependent and extended regularly varying-tailed claims.Following this work,the authors obtain a weakl...In 2007,Chen and Ng investigated infinite-time ruin probability with constant interest forceand negatively quadrant dependent and extended regularly varying-tailed claims.Following this work,the authors obtain a weakly asymptotic equivalent formula for the finite-time and infinite-time ruinprobability with constant interest force,negatively quadrant dependent,and dominated varying-tailedclaims and negatively lower orthant dependent inter-arrival times.In particular,when the claims areconsistently varying-tailed,an asymptotic equivalent formula is presented.展开更多
In this paper, Kolmogorov-type inequality for negatively superadditive dependent （NSD） random variables is established. By using this inequality, we obtain the almost sure convergence for NSD sequences, which extend...In this paper, Kolmogorov-type inequality for negatively superadditive dependent （NSD） random variables is established. By using this inequality, we obtain the almost sure convergence for NSD sequences, which extends the corresponding results for independent sequences and negatively associated （NA） sequences. In addition, the strong stability for weighted sums of NSD random variables is studied.展开更多
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）.
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Supported by National Natural Science Foundation of China(Grant Nos.11401415 and 11571250)
文摘In this paper, the complete convergence and complete moment convergence for maximal weighted sums of extended negatively dependent random variables are investigated. Some sufficient conditions for the convergence are provided. In addition, the Marcinkiewicz Zygmund type strong law of large numbers for weighted sums of extended negatively dependent random variables is obtained. The results obtained in the article extend the corresponding ones for independent random variables and some dependent random variables.
基金Supported by the NSF of Anhui Province(1308085QA03,1408085QA02,1208085QA03)Supported by the Youth Science Research Fund of Anhui University+1 种基金Supported by the Students Innovative Training Project of Anhui University(201410357118)Supported by the Students Science Research Training Program of Anhui University(kyxl2013003)
文摘Some exponential inequalities and complete convergence are established for extended negatively dependent(END) random variables. The inequalities extend and improve the results of Kim and Kim(On the exponential inequality for negative dependent sequence.Communications of the Korean Mathematical Society, 2007, 22(2): 315-321) and Nooghabi and Azarnoosh(Exponential inequality for negatively associated random variables. Statistical Papers, 2009, 50(2): 419-428). We also obtain the convergence rate O(n-1/2ln1/2n) for the strong law of large numbers, which improves the corresponding ones of Kim and Kim,and Nooghabi and Azarnoosh.
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Acknowledgements This work was supported by the National Natural Science Foundation of China （Grant No. 11071182）.
文摘We establish some strong limit theorems for a sequence of pair-wise extended lower/upper negatively dependent random variables and give some new examples of dependent random variables.
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 Project of the Feature Specialty of China(TS11496)Supported by the Scientific Research Projects of Fuyang Teacher’s College(2009FSKJ09)
文摘Some probability inequalities are established for extended negatively dependent(END) random variables. The inequalities extend some corresponding ones for negatively associated random variables and negatively orthant dependent random variables. By using these probability inequalities, we further study the complete convergence for END random variables. We also obtain the convergence rate O(n-1/2ln1/2n) for the strong law of large numbers, which generalizes and improves the corresponding ones for some known results.
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Foundation of Anhui Educational Committee(No.KJ2013Z225)
文摘In the paper,we get the precise results of Hájek-Rényi type inequalities for the partial sums of negatively orthant dependent sequences,which improve the results of Theorem 3.1and Corollary 3.2 in Kim(2006)and the strong law of large numbers and strong growth rate for negatively orthant dependent sequences.
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This research is supported by National Science Foundation of China under Grant No. 10671139 and the Science Foundation of Jiangsu Province under Grant No. 11071182.
文摘This paper establishes some asymptotic formulas for the infinite-time ruin probabilities of two kinds of dependent risk models. One risk model considers the claim sizes as a modulated process, and the other deals with negatively upper orthant dependent claim sizes. In the two models, the inter-arrival times are both assumed to be negatively lower orthant dependent.
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.
基金supported by the National Natural Science Foundation of China under Grant Nos.11671012 and 11871072the Natural Science Foundation of Anhui Province under Grant Nos.1808085QA03,1908085QA01,1908085QA07+1 种基金the Provincial Natural Science Research Project of Anhui Colleges under Grant No.KJ2019A0003the Students Innovative Training Project of Anhui University under Grant No.201910357002。
文摘This paper mainly studies the strong convergence properties for weighted sums of extended negatively dependent(END,for short)random variables.Some sufficient conditions to prove the strong law of large numbers for weighted sums of END random variables are provided.In particular,the authors obtain the weighted version of Kolmogorov type strong law of large numbers for END random variables as a product.The results that the authors obtained generalize the corresponding ones for independent random variables and some dependent random variables.As an application,the authors investigate the errors-in-variables(EV,for short)regression models and establish the strong consistency for the least square estimators.Simulation studies are conducted to demonstrate the performance of the proposed procedure and a real example is analysed for illustration.
基金supported by the National Science Foundation of China under Grant No. 10671139.
文摘In 2007,Chen and Ng investigated infinite-time ruin probability with constant interest forceand negatively quadrant dependent and extended regularly varying-tailed claims.Following this work,the authors obtain a weakly asymptotic equivalent formula for the finite-time and infinite-time ruinprobability with constant interest force,negatively quadrant dependent,and dominated varying-tailedclaims and negatively lower orthant dependent inter-arrival times.In particular,when the claims areconsistently varying-tailed,an asymptotic equivalent formula is presented.
基金Supported by National Natural Science Foundation of China(Grant Nos.11171001,11201001 and 11126176)Natural Science Foundation of Anhui Province(1208085QA03)Academic Innovation Team of Anhui University(Grant No.KJTD001B)
文摘In this paper, Kolmogorov-type inequality for negatively superadditive dependent （NSD） random variables is established. By using this inequality, we obtain the almost sure convergence for NSD sequences, which extends the corresponding results for independent sequences and negatively associated （NA） sequences. In addition, the strong stability for weighted sums of NSD random variables is studied.
