The results of Bryc on large deviations for empirical measures of stationary Φ-mixing sequences are extended. Bryc states his results in the usual weak topology on the space ofprobability measures. In this paper, und...The results of Bryc on large deviations for empirical measures of stationary Φ-mixing sequences are extended. Bryc states his results in the usual weak topology on the space ofprobability measures. In this paper, under somewhat weaker assumptions than those of Bryc,the author extends Bryc's results by taking the finer topology which is generated by the integralsover bounded measurable functions.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
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
Let {Xi}i=1^∞ be a standardized stationary Gaussian sequence with covariance function τ（n） =EX1Xn＋1, Sn =∑i=1^nXi,and X^-n=Sn/n.And let Nn be the point process formed by the exceedances of random level （x/√2 l...Let {Xi}i=1^∞ be a standardized stationary Gaussian sequence with covariance function τ（n） =EX1Xn＋1, Sn =∑i=1^nXi,and X^-n=Sn/n.And let Nn be the point process formed by the exceedances of random level （x/√2 log n＋√2 log n-log（4π log n）/2√log n） √1-τ（n） ＋ X^-n by X1,X2,…, Xn. Under some mild conditions, Nn and Sn are asymptotically independent, and Nn converges weakly to a Poisson process on （0,1].展开更多
In this paper,we study the asymptotic relation between the first crossing point and the last exit time for Gaussian order statistics which are generated by stationary weakly and strongly dependent Gaussian sequences.I...In this paper,we study the asymptotic relation between the first crossing point and the last exit time for Gaussian order statistics which are generated by stationary weakly and strongly dependent Gaussian sequences.It is shown that the first crossing point and the last exit time are asymptotically independent and dependent for weakly and strongly dependent cases,respectively.The asymptotic relations between the first crossing point and the last exit time for stationary weakly and strongly dependent Gaussian sequences are also obtained.展开更多
Let {Xkl,…, Xkp, k≥ 1} be a p-dimensional standard （zero-means, unit-variances）non-stationary Gaussian vector sequence. In this work, the joint limit distribution of the maximaof {Xkl,…, Xkp, k 〉 1}, the incompl...Let {Xkl,…, Xkp, k≥ 1} be a p-dimensional standard （zero-means, unit-variances）non-stationary Gaussian vector sequence. In this work, the joint limit distribution of the maximaof {Xkl,…, Xkp, k 〉 1}, the incomplete maxima of those sequences subject to random failureand the partial sums of those sequences are obtained.展开更多
Considering a sequence of standardized stationary Gaussian random variables, a universal result in the almost sure central limit theorem for maxima and partial sum is established. Our result generalizes and improves t...Considering a sequence of standardized stationary Gaussian random variables, a universal result in the almost sure central limit theorem for maxima and partial sum is established. Our result generalizes and improves that on the almost sure central limit theory previously obtained by Marcin Dudzinski [1]. Our result reaches the optimal form.展开更多
This paper investigates the problem of almost sure limit theorem for the maximum of quasi-stationary sequence based on the result of Turkman and Walker. We prove an almost sure limit theorem for the maximum of a class...This paper investigates the problem of almost sure limit theorem for the maximum of quasi-stationary sequence based on the result of Turkman and Walker. We prove an almost sure limit theorem for the maximum of a class of quasi-stationary sequence under weak dependence conditions of D （uk, un） and αtm,ln = 0 （（log log n）-（1＋ε））.展开更多
Let （Xi） be a martingale difference sequence and Sn=∑^ni=1Xi Suppose （Xi） i=1 is bounded in L^p. In the case p ≥2, Lesigne and Volny （Stochastic Process. Appl. 96 （2001） 143） obtained the estimation μ（Sn ...Let （Xi） be a martingale difference sequence and Sn=∑^ni=1Xi Suppose （Xi） i=1 is bounded in L^p. In the case p ≥2, Lesigne and Volny （Stochastic Process. Appl. 96 （2001） 143） obtained the estimation μ（Sn 〉 n） ≤ cn^-p/2, Yulin Li （Statist. Probab. Lett. 62 （2003） 317） generalized the result to the case when p ∈ （1,2] and obtained μ（Sn 〉 n） ≤ cn^l-p, these are optimal in a certain sense. In this article, the authors study the large deviation of Sn for some dependent sequences and obtain the same order optimal upper bounds for μ（Sn 〉 n） as those for martingale difference sequence.展开更多
Let {X n , n ≥ 1} be an arbitrary sequence of random variables. Some convergence results for the partial sums of arbitrary sequence of random variables are obtained, which generalize the known results for independent...Let {X n , n ≥ 1} be an arbitrary sequence of random variables. Some convergence results for the partial sums of arbitrary sequence of random variables are obtained, which generalize the known results for independent sequences, NA sequences, ρ-mixing sequences and φ-mixing sequences, and so on.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
Assume that {X n } is a strictly stationary β-mixing random sequence with the β-mixing coefficient β k = O(k ?r ), 0 < r ? 1. Yu (1994) obtained convergence rates of empirical processes of strictly stationary β...Assume that {X n } is a strictly stationary β-mixing random sequence with the β-mixing coefficient β k = O(k ?r ), 0 < r ? 1. Yu (1994) obtained convergence rates of empirical processes of strictly stationary β-mixing random sequence indexed by bounded classes of functions. Here, a new truncation method is proposed and used to study the convergence for empirical processes of strictly stationary β-mixing sequences indexed by an unbounded class of functions. The research results show that if the envelope of the index class of functions is in L p, p > 2 or p > 4, uniform convergence rates of empirical processes of strictly stationary β-mixing random sequence over the index classes can reach O((n r/(1+r)/log n)?1/2) or O((n r/(1+r)/log n)?3/4) and that the Central Limit Theorem does not always hold for the empirical processes.展开更多
在全球气候变化和高强度人类活动的共同影响下,许多流域天然水循环过程受到破坏。径流序列呈现明显的非平稳特性,给水资源规划、管理、预测和调控带来一定的挑战。揭示径流序列的非平稳特性可以有效应对全球气候变化下的复杂水问题,对...在全球气候变化和高强度人类活动的共同影响下,许多流域天然水循环过程受到破坏。径流序列呈现明显的非平稳特性,给水资源规划、管理、预测和调控带来一定的挑战。揭示径流序列的非平稳特性可以有效应对全球气候变化下的复杂水问题,对降低水文分析难度和提高径流预测精度具有十分重要的意义。研究以汾河上游兰村站为研究对象,分析该站1958-2016年年径流和月径流序列是否平稳。首先从随机水文学角度,采用Mann-Kendall检验法和小波分析法识别径流序列的趋势、突变和周期特征。在此基础上,从统计水文学角度引入Ng-Perron单位根检验方法。通过Mann-Kendall趋势检验和散点图法选择合适的检验方程,对径流序列进行广义最小二乘法(Generalized Least Squares,GLS)退势,并利用修正的信息准则(Modified information criterion,MIC)计算最优时间滞后阶数,判别径流序列是否具有非平稳性。结果显示,径流序列存在趋势、突变和周期成分,为非平稳径流序列。同时Ng-Perron单位根检验表明,该站年、月径流序列在1%显著性水平上具有非平稳特性。相较传统单位根检验方法,Ng-Perron单位根检验采用更为稳健的修正检验统计量,显著调整小样本情况下水平扭曲的现象,具有更好检验水平和功效,因而可以得到更合理的检验结果。研究成果为径流序列非平稳性检验理论的进一步改进及径流预测模型发展与应用提供参考。展开更多
基金Project supported by the National Natural Science Foundation of China
文摘The results of Bryc on large deviations for empirical measures of stationary Φ-mixing sequences are extended. Bryc states his results in the usual weak topology on the space ofprobability measures. In this paper, under somewhat weaker assumptions than those of Bryc,the author extends Bryc's results by taking the finer topology which is generated by the integralsover bounded measurable functions.
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.
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.
基金Supported by the Program for Excellent Talents in Chongqing Higher Education Institutions (120060-20600204)
文摘Let {Xi}i=1^∞ be a standardized stationary Gaussian sequence with covariance function τ（n） =EX1Xn＋1, Sn =∑i=1^nXi,and X^-n=Sn/n.And let Nn be the point process formed by the exceedances of random level （x/√2 log n＋√2 log n-log（4π log n）/2√log n） √1-τ（n） ＋ X^-n by X1,X2,…, Xn. Under some mild conditions, Nn and Sn are asymptotically independent, and Nn converges weakly to a Poisson process on （0,1].
基金Supported by the National Natural Science Foundation of China(11501250)Zhejiang Provincial Natural Science Foundation of China(LY18A010020)Innovation of Jiaxing City:a program to support the talented persons。
文摘In this paper,we study the asymptotic relation between the first crossing point and the last exit time for Gaussian order statistics which are generated by stationary weakly and strongly dependent Gaussian sequences.It is shown that the first crossing point and the last exit time are asymptotically independent and dependent for weakly and strongly dependent cases,respectively.The asymptotic relations between the first crossing point and the last exit time for stationary weakly and strongly dependent Gaussian sequences are also obtained.
基金Supported by the National Natural Science Foundation of China(11326175,71471090)the Zhejiang Natural Science Foundation of China(LQ14A010012)
文摘Let {Xkl,…, Xkp, k≥ 1} be a p-dimensional standard （zero-means, unit-variances）non-stationary Gaussian vector sequence. In this work, the joint limit distribution of the maximaof {Xkl,…, Xkp, k 〉 1}, the incomplete maxima of those sequences subject to random failureand the partial sums of those sequences are obtained.
文摘Considering a sequence of standardized stationary Gaussian random variables, a universal result in the almost sure central limit theorem for maxima and partial sum is established. Our result generalizes and improves that on the almost sure central limit theory previously obtained by Marcin Dudzinski [1]. Our result reaches the optimal form.
基金Project supported by the National Natural Science Foundation of China(11171275)the Natural Science Foundation Project of CQ(cstc2012jjA00029)Liaocheng University Foundation(X09005)
文摘This paper investigates the problem of almost sure limit theorem for the maximum of quasi-stationary sequence based on the result of Turkman and Walker. We prove an almost sure limit theorem for the maximum of a class of quasi-stationary sequence under weak dependence conditions of D （uk, un） and αtm,ln = 0 （（log log n）-（1＋ε））.
基金the National Natural Science Foundation of China(10571001)the Innovation Group Foundation of Anhui University
文摘Let （Xi） be a martingale difference sequence and Sn=∑^ni=1Xi Suppose （Xi） i=1 is bounded in L^p. In the case p ≥2, Lesigne and Volny （Stochastic Process. Appl. 96 （2001） 143） obtained the estimation μ（Sn 〉 n） ≤ cn^-p/2, Yulin Li （Statist. Probab. Lett. 62 （2003） 317） generalized the result to the case when p ∈ （1,2] and obtained μ（Sn 〉 n） ≤ cn^l-p, these are optimal in a certain sense. In this article, the authors study the large deviation of Sn for some dependent sequences and obtain the same order optimal upper bounds for μ（Sn 〉 n） as those for martingale difference sequence.
基金Supported by the National Natural Science Foundation of China(10871001)Supported by the Provincial Natural Science Research Project of Anhui Colleges(KJ2010A005)+1 种基金Supported by the Talents Youth Fund of Anhui Province Universities(2010SQRL016ZD)Supported by the Youth Science Research Fund of Anhui University(2009QN011A)
文摘Let {X n , n ≥ 1} be an arbitrary sequence of random variables. Some convergence results for the partial sums of arbitrary sequence of random variables are obtained, which generalize the known results for independent sequences, NA sequences, ρ-mixing sequences and φ-mixing sequences, and so on.
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This work was supported partially by the NationalNatural Science Foundation of China (Grant No. 19661001) the Natural Science Foundation of Guangdong Education Committee.
文摘Assume that {X n } is a strictly stationary β-mixing random sequence with the β-mixing coefficient β k = O(k ?r ), 0 < r ? 1. Yu (1994) obtained convergence rates of empirical processes of strictly stationary β-mixing random sequence indexed by bounded classes of functions. Here, a new truncation method is proposed and used to study the convergence for empirical processes of strictly stationary β-mixing sequences indexed by an unbounded class of functions. The research results show that if the envelope of the index class of functions is in L p, p > 2 or p > 4, uniform convergence rates of empirical processes of strictly stationary β-mixing random sequence over the index classes can reach O((n r/(1+r)/log n)?1/2) or O((n r/(1+r)/log n)?3/4) and that the Central Limit Theorem does not always hold for the empirical processes.
文摘在全球气候变化和高强度人类活动的共同影响下,许多流域天然水循环过程受到破坏。径流序列呈现明显的非平稳特性,给水资源规划、管理、预测和调控带来一定的挑战。揭示径流序列的非平稳特性可以有效应对全球气候变化下的复杂水问题,对降低水文分析难度和提高径流预测精度具有十分重要的意义。研究以汾河上游兰村站为研究对象,分析该站1958-2016年年径流和月径流序列是否平稳。首先从随机水文学角度,采用Mann-Kendall检验法和小波分析法识别径流序列的趋势、突变和周期特征。在此基础上,从统计水文学角度引入Ng-Perron单位根检验方法。通过Mann-Kendall趋势检验和散点图法选择合适的检验方程,对径流序列进行广义最小二乘法(Generalized Least Squares,GLS)退势,并利用修正的信息准则(Modified information criterion,MIC)计算最优时间滞后阶数,判别径流序列是否具有非平稳性。结果显示,径流序列存在趋势、突变和周期成分,为非平稳径流序列。同时Ng-Perron单位根检验表明,该站年、月径流序列在1%显著性水平上具有非平稳特性。相较传统单位根检验方法,Ng-Perron单位根检验采用更为稳健的修正检验统计量,显著调整小样本情况下水平扭曲的现象,具有更好检验水平和功效,因而可以得到更合理的检验结果。研究成果为径流序列非平稳性检验理论的进一步改进及径流预测模型发展与应用提供参考。
