In this paper, a notion of negative side ρ \|mixing ( ρ\+- \|mixing) which can be regarded as asymptotic negative association is defined, and some Rosenthal type inequalities for ρ\+- \|mixing random fields are est...In this paper, a notion of negative side ρ \|mixing ( ρ\+- \|mixing) which can be regarded as asymptotic negative association is defined, and some Rosenthal type inequalities for ρ\+- \|mixing random fields are established. The complete convergence and almost sure summability on the convergence rates with respect to the strong law of large numbers are also discussed for ρ\+-\| mixing random fields. The results obtained extend those for negatively associated sequences and ρ\+*\| mixing random fields.展开更多
In this paper, we establish some Rosenthal type inequalities for maximum partial sums of asymptotically almost negatively associated random variables, which extend the corresponding results for negatively associated r...In this paper, we establish some Rosenthal type inequalities for maximum partial sums of asymptotically almost negatively associated random variables, which extend the corresponding results for negatively associated random variables. As applications of these inequalities, by employing the notions of residual Cesàro α-integrability and strong residual Cesàro α-integrability, we derive some results on Lp convergence where 1 < p < 2 and complete convergence. In addition, we estimate the rate of convergence in Marcinkiewicz-Zygmund strong law for partial sums of identically distributed random variables.展开更多
In this paper, we discuss the moving-average process Xk = ∑i=-∞ ^∞ ai＋kεi, where {εi;-∞ 〈 i 〈 ∞} is a doubly infinite sequence of identically distributed ψ-mixing or negatively associated random variables w...In this paper, we discuss the moving-average process Xk = ∑i=-∞ ^∞ ai＋kεi, where {εi;-∞ 〈 i 〈 ∞} is a doubly infinite sequence of identically distributed ψ-mixing or negatively associated random variables with mean zeros and finite variances, {ai;-∞ 〈 i 〈 -∞） is an absolutely solutely summable sequence of real numbers.展开更多
Negatively associated sequences have been studied extensively in recent years, Asymptotically negative association is a generalization of negative association, In this paper a Berry Esseen theorem and a law of the ite...Negatively associated sequences have been studied extensively in recent years, Asymptotically negative association is a generalization of negative association, In this paper a Berry Esseen theorem and a law of the iterated logarithm are obtained for asymptotically negatively associated sequences.展开更多
Empirical Euclidean likelihood for general estimating equations for association dependent processes is investigated. The strong consistency and asymptotic normality of the blockwise maximum empirical Euclidean likelih...Empirical Euclidean likelihood for general estimating equations for association dependent processes is investigated. The strong consistency and asymptotic normality of the blockwise maximum empirical Euclidean likelihood estimator are presented. We show that it is more efficient than estimator without blocking. The blockwise empirical Euclidean log-likelihood ratio asymptotically follows a chi-square distribution.展开更多
该文主要讨论的是滑线性过程X_k=sum from i=-∞to∞a_(i+k)ε_i,其中{ε_i；-∞＜i＜∞}是均值为零,方差有限的双测无穷同分布■-混合或负相伴随机变量序列,{a_i；～∞＜i＜∞}为绝对可和的实数序列．令S_n=sum from k=1 to n X_k,n≥1...该文主要讨论的是滑线性过程X_k=sum from i=-∞to∞a_(i+k)ε_i,其中{ε_i；-∞＜i＜∞}是均值为零,方差有限的双测无穷同分布■-混合或负相伴随机变量序列,{a_i；～∞＜i＜∞}为绝对可和的实数序列．令S_n=sum from k=1 to n X_k,n≥1,作者证明了,对于1≤p＜2以及r＞p,若E|ε_1|~r＜∞■ε^(2(r-p)/(2-p))sum from n=1 to∞n^(r/p-2)P{|S_n|≥εn^(1/p)}=p/(r-p)E|Z|^(2(r-p)/(2-p)),其中Z是服从均值为零,方差为τ~2=σ~2·(sum from i=-∞to∞．a_i)~2的正态分布．展开更多
Background:Ecological processes such as seedling establishment,biotic interactions,and mortality can leave footprints on species spatial structure that can be detectable through spatial point-pattern analysis(SPPA).Be...Background:Ecological processes such as seedling establishment,biotic interactions,and mortality can leave footprints on species spatial structure that can be detectable through spatial point-pattern analysis(SPPA).Being widely used in plant ecology,SPPA is increasingly carried out to describe biotic interactions and interpret patternprocess relationships.However,some aspects are still subjected to a non-negligible debate such as required sample size(in terms of the number of points and plot area),the link between the low number of points and frequently observed random(or independent)patterns,and relating patterns to processes.In this paper,an overview of SPPA is given based on rich and updated literature providing guidance for ecologists(especially beginners)on summary statistics,uni-/bi-/multivariate analysis,unmarked/marked analysis,types of marks,etc.Some ambiguities in SPPA are also discussed.Results:SPPA has a long history in plant ecology and is based on a large set of summary statistics aiming to describe species spatial patterns.Several mechanisms known to be responsible for species spatial patterns are actually investigated in different biomes and for different species.Natural processes,plant environmental conditions,and human intervention are interrelated and are key drivers of plant spatial distribution.In spite of being not recommended,small sample sizes are more common in SPPA.In some areas,periodic forest inventories and permanent plots are scarce although they are key tools for spatial data availability and plant dynamic monitoring.Conclusion:The spatial position of plants is an interesting source of information that helps to make hypotheses about processes responsible for plant spatial structures.Despite the continuous progress of SPPA,some ambiguities require further clarifications.展开更多
文摘In this paper, a notion of negative side ρ \|mixing ( ρ\+- \|mixing) which can be regarded as asymptotic negative association is defined, and some Rosenthal type inequalities for ρ\+- \|mixing random fields are established. The complete convergence and almost sure summability on the convergence rates with respect to the strong law of large numbers are also discussed for ρ\+-\| mixing random fields. The results obtained extend those for negatively associated sequences and ρ\+*\| mixing random fields.
基金supported by National Natural Science Foundation of China (Grant No.10871217) the SCR of Chongqing Municipal Education Commission (Grant No.KJ090703)
文摘In this paper, we establish some Rosenthal type inequalities for maximum partial sums of asymptotically almost negatively associated random variables, which extend the corresponding results for negatively associated random variables. As applications of these inequalities, by employing the notions of residual Cesàro α-integrability and strong residual Cesàro α-integrability, we derive some results on Lp convergence where 1 < p < 2 and complete convergence. In addition, we estimate the rate of convergence in Marcinkiewicz-Zygmund strong law for partial sums of identically distributed random variables.
基金Research supported by National Natural Science Foundation of China
文摘In this paper, we discuss the moving-average process Xk = ∑i=-∞ ^∞ ai＋kεi, where {εi;-∞ 〈 i 〈 ∞} is a doubly infinite sequence of identically distributed ψ-mixing or negatively associated random variables with mean zeros and finite variances, {ai;-∞ 〈 i 〈 -∞） is an absolutely solutely summable sequence of real numbers.
基金National Natural Science Foundation of China(No.10471126)
文摘Negatively associated sequences have been studied extensively in recent years, Asymptotically negative association is a generalization of negative association, In this paper a Berry Esseen theorem and a law of the iterated logarithm are obtained for asymptotically negatively associated sequences.
基金Supported by the National Natural Science Foundation of China (10771192)the Zhejiang Natural Science Foundation (J20091364)
文摘Empirical Euclidean likelihood for general estimating equations for association dependent processes is investigated. The strong consistency and asymptotic normality of the blockwise maximum empirical Euclidean likelihood estimator are presented. We show that it is more efficient than estimator without blocking. The blockwise empirical Euclidean log-likelihood ratio asymptotically follows a chi-square distribution.
文摘该文主要讨论的是滑线性过程X_k=sum from i=-∞to∞a_(i+k)ε_i,其中{ε_i；-∞＜i＜∞}是均值为零,方差有限的双测无穷同分布■-混合或负相伴随机变量序列,{a_i；～∞＜i＜∞}为绝对可和的实数序列．令S_n=sum from k=1 to n X_k,n≥1,作者证明了,对于1≤p＜2以及r＞p,若E|ε_1|~r＜∞■ε^(2(r-p)/(2-p))sum from n=1 to∞n^(r/p-2)P{|S_n|≥εn^(1/p)}=p/(r-p)E|Z|^(2(r-p)/(2-p)),其中Z是服从均值为零,方差为τ~2=σ~2·(sum from i=-∞to∞．a_i)~2的正态分布．
文摘Background:Ecological processes such as seedling establishment,biotic interactions,and mortality can leave footprints on species spatial structure that can be detectable through spatial point-pattern analysis(SPPA).Being widely used in plant ecology,SPPA is increasingly carried out to describe biotic interactions and interpret patternprocess relationships.However,some aspects are still subjected to a non-negligible debate such as required sample size(in terms of the number of points and plot area),the link between the low number of points and frequently observed random(or independent)patterns,and relating patterns to processes.In this paper,an overview of SPPA is given based on rich and updated literature providing guidance for ecologists(especially beginners)on summary statistics,uni-/bi-/multivariate analysis,unmarked/marked analysis,types of marks,etc.Some ambiguities in SPPA are also discussed.Results:SPPA has a long history in plant ecology and is based on a large set of summary statistics aiming to describe species spatial patterns.Several mechanisms known to be responsible for species spatial patterns are actually investigated in different biomes and for different species.Natural processes,plant environmental conditions,and human intervention are interrelated and are key drivers of plant spatial distribution.In spite of being not recommended,small sample sizes are more common in SPPA.In some areas,periodic forest inventories and permanent plots are scarce although they are key tools for spatial data availability and plant dynamic monitoring.Conclusion:The spatial position of plants is an interesting source of information that helps to make hypotheses about processes responsible for plant spatial structures.Despite the continuous progress of SPPA,some ambiguities require further clarifications.
