By using a Rosenthal type inequality established in this paper, the complete convergence and almost sure summability on the convergence rates with respect to the strong law of large numbers are discussed for *-mixing...By using a Rosenthal type inequality established in this paper, the complete convergence and almost sure summability on the convergence rates with respect to the strong law of large numbers are discussed for *-mixing random fields.展开更多
This paper discusses complete convergence properties of the sums of -mixing random sequences.As a result,we improve the corresponding results of Wu Qunying(2001). And extended the Baum and Katz complete convergence ...This paper discusses complete convergence properties of the sums of -mixing random sequences.As a result,we improve the corresponding results of Wu Qunying(2001). And extended the Baum and Katz complete convergence to the case of -mixing random sequences by moment inequality and truncating without necessarily adding any extra conditions.展开更多
In this paper, strong laws of large numbers for weighted sums of ■-mixing sequence are investigated. Our results extend the corresponding results for negatively associated sequence to the case of ■-mixing sequence.
We give some theorems of strong law of large numbers and complete convergence for sequences of φ-mixing random variables. In particular, Wittmann＇s strong law of large numbers and Teicher＇s strong law of large nnum...We give some theorems of strong law of large numbers and complete convergence for sequences of φ-mixing random variables. In particular, Wittmann＇s strong law of large numbers and Teicher＇s strong law of large nnumbers for independent random variables are generalized to the case of φ -minxing random variables.展开更多
In this paper, we will present some strong convergence results for sequences of ψ-mixing random variables. The results for sequences of ψ-mixing random variables generalize the corresponding results for independent ...In this paper, we will present some strong convergence results for sequences of ψ-mixing random variables. The results for sequences of ψ-mixing random variables generalize the corresponding results for independent random variable sequences without any extra conditions.展开更多
In this paper,we establish a Rosenthal-type inequality of partial sums for ρ~mixing random variables.As its applications,we get the complete convergence rates in the strong laws for ρ^-mixing random variables.The re...In this paper,we establish a Rosenthal-type inequality of partial sums for ρ~mixing random variables.As its applications,we get the complete convergence rates in the strong laws for ρ^-mixing random variables.The result obtained extends the corresponding result.展开更多
In the paper,we study the strong uniform consistency for the kernal estimates of random window w■th of density function and its derivatives under the condition that the sequence{X_n}of the ■ are the identically Φ-m...In the paper,we study the strong uniform consistency for the kernal estimates of random window w■th of density function and its derivatives under the condition that the sequence{X_n}of the ■ are the identically Φ-mixing random variabks.展开更多
In this paper, we investigate the nonparametric regression model based on ρ-mixing errors, which are stochastically dominated by a nonnegative random variable. Weobtain the convergence rate for the weighted estimator...In this paper, we investigate the nonparametric regression model based on ρ-mixing errors, which are stochastically dominated by a nonnegative random variable. Weobtain the convergence rate for the weighted estimator of unknown function g（x） in pth-mean, which yields the convergence rate in probability. Moreover, an example of the nearestneighbor estimator is also illustrated and the convergence rates of estimator are presented.展开更多
In this paper, we give some conditions on diverging rate of series of the probabilities and converging rate of series of the α-mixing coefficients for sequences of events, under which the conclusion of the Second Bor...In this paper, we give some conditions on diverging rate of series of the probabilities and converging rate of series of the α-mixing coefficients for sequences of events, under which the conclusion of the Second Borel-Cantelli Lemma holds. As corollaries, some moment conditions are obtained, under which the strong law of large numbers holds for sequences of identically distributed random variables.展开更多
The strong consistency of M estimator of regression parameter in linear model for φ-mixing samples is discussed by using the classic Rosenthal type inequality. We get the strong consistency of M estimator under lower...The strong consistency of M estimator of regression parameter in linear model for φ-mixing samples is discussed by using the classic Rosenthal type inequality. We get the strong consistency of M estimator under lower moment condition, which generalizes and improves the corresponding ones for independent sequences.展开更多
Hu Shuhe gets a sufficient condition on the law of the iterated logarithm for the sums of φ-mixing sequences with duple suffixes. This paper greatly improves his condition.
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...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 of independent sequence with identical distribution to the case of φ-mixing sequence with different distribution.展开更多
In this paper, the complete convergence and weak law of large numbers are established for ρ-mixing sequences of random variables. Our results extend and improve the Baum and Katz complete convergence theorem and the ...In this paper, the complete convergence and weak law of large numbers are established for ρ-mixing sequences of random variables. Our results extend and improve the Baum and Katz complete convergence theorem and the classical weak law of large numbers, etc. from independent sequences of random variables to ρ-mixing sequences of random variables without necessarily adding any extra conditions.展开更多
Let be a strictly stationary sequence of ρ?-mixing random variables. We proved the almost sure central limit theorem, containing the general weight sequences, for the partial sums , where , . The result generalizes a...Let be a strictly stationary sequence of ρ?-mixing random variables. We proved the almost sure central limit theorem, containing the general weight sequences, for the partial sums , where , . The result generalizes and improves the previous results.展开更多
基金National Natural Science Foundation of China! (No. 19701O11) Foundation of "151 talent project" of Zhejiang provience.
文摘By using a Rosenthal type inequality established in this paper, the complete convergence and almost sure summability on the convergence rates with respect to the strong law of large numbers are discussed for *-mixing random fields.
基金Supported by the National Natural Science Foundation of China（11061012） Supported by the Natural Science Foundation of Guangxi（2010GXNSFA013121）
文摘This paper discusses complete convergence properties of the sums of -mixing random sequences.As a result,we improve the corresponding results of Wu Qunying(2001). And extended the Baum and Katz complete convergence to the case of -mixing random sequences by moment inequality and truncating without necessarily adding any extra conditions.
基金Foundation item： Supported by the National Natural Science Foundation of China（11171001, 11201001） Supported by the Natural Science Foundation of Anhui Province（t208085QA03, 1308085QA03）
文摘In this paper, strong laws of large numbers for weighted sums of ■-mixing sequence are investigated. Our results extend the corresponding results for negatively associated sequence to the case of ■-mixing sequence.
基金Supported by the National Natural Science Foundation of China (10671149)
文摘We give some theorems of strong law of large numbers and complete convergence for sequences of φ-mixing random variables. In particular, Wittmann＇s strong law of large numbers and Teicher＇s strong law of large nnumbers for independent random variables are generalized to the case of φ -minxing random variables.
基金Supported by the University Students Science Research Training Program of Anhui University(KYXL20110004)
文摘In this paper, we will present some strong convergence results for sequences of ψ-mixing random variables. The results for sequences of ψ-mixing random variables generalize the corresponding results for independent random variable sequences without any extra conditions.
基金Supported by the National Science Foundation（10661006） Supported by Innovation Project of Guangxi Graduate Education（2007105960812M18）
文摘In this paper,we establish a Rosenthal-type inequality of partial sums for ρ~mixing random variables.As its applications,we get the complete convergence rates in the strong laws for ρ^-mixing random variables.The result obtained extends the corresponding result.
基金supported by Natural Science Foun■ion of Henan P■visial Commission of Bdusation
文摘In the paper,we study the strong uniform consistency for the kernal estimates of random window w■th of density function and its derivatives under the condition that the sequence{X_n}of the ■ are the identically Φ-mixing random variabks.
基金Supported by National Natural Science Foundation of China(11426032,11501005)Natural Science Foundation of Anhui Province(1408085QA02,1508085QA01,1508085J06)+5 种基金Provincial Natural Science Research Project of Anhui Colleges(KJ2014A010,KJ2014A020,KJ2015A065)Higher Education Talent Revitalization Project of Anhui Province(2013SQRL005ZD)Quality Engineering Project of Anhui Province(2015jyxm054,2015jyxm057)Students Science Research Training Program of Anhui University(KYXL2014016,KYXL2014013)Applied Teaching Model Curriculum of Anhui University(XJYYKC1401,ZLTS2015052,ZLTS2015053)Doctoral Research Start-up Funds Projects of Anhui University
文摘In this paper, we investigate the nonparametric regression model based on ρ-mixing errors, which are stochastically dominated by a nonnegative random variable. Weobtain the convergence rate for the weighted estimator of unknown function g（x） in pth-mean, which yields the convergence rate in probability. Moreover, an example of the nearestneighbor estimator is also illustrated and the convergence rates of estimator are presented.
基金Supported by the SCR of Chongqing Municipal Education Commission(KJ090703)
文摘In this paper, we give some conditions on diverging rate of series of the probabilities and converging rate of series of the α-mixing coefficients for sequences of events, under which the conclusion of the Second Borel-Cantelli Lemma holds. As corollaries, some moment conditions are obtained, under which the strong law of large numbers holds for sequences of identically distributed random variables.
基金The NSF (11201001,11171001,11126176) of Chinathe NSF (1208085QA03) of Anhui Province+2 种基金Provincial Natural Science Research Project (KJ2010A005) of Anhui CollegesDoctoral Research Start-up Funds Projects of Anhui Universitythe Students’ Innovative Training Project (2012003) of Anhui University
文摘The strong consistency of M estimator of regression parameter in linear model for φ-mixing samples is discussed by using the classic Rosenthal type inequality. We get the strong consistency of M estimator under lower moment condition, which generalizes and improves the corresponding ones for independent sequences.
文摘Hu Shuhe gets a sufficient condition on the law of the iterated logarithm for the sums of φ-mixing sequences with duple suffixes. This paper greatly improves his condition.
基金Supported by the National Natural Science Foundation of China（11671012, 11526033, 11501004, 11501005） Supported by the Natural Science Foundation of Anhui Province（1608085QA02） Supported by the Science Fund for Distinguished Young Scholars of Anhui Province（1508085J06）
文摘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 of independent sequence with identical distribution to the case of φ-mixing sequence with different distribution.
文摘In this paper, the complete convergence and weak law of large numbers are established for ρ-mixing sequences of random variables. Our results extend and improve the Baum and Katz complete convergence theorem and the classical weak law of large numbers, etc. from independent sequences of random variables to ρ-mixing sequences of random variables without necessarily adding any extra conditions.
基金supported by National Natural Science Foundation of China(11361019).
文摘Let be a strictly stationary sequence of ρ?-mixing random variables. We proved the almost sure central limit theorem, containing the general weight sequences, for the partial sums , where , . The result generalizes and improves the previous results.
