A Note on Strong Convergence of Sums of Dependent Random Variables

For a sequence of dependent square-integrable random variables and a sequence of positive constants {bn,  n≥1}, conditions are provided under which the series ∑i=1n(Xi−EXi)/bi converges almost surely as n→∞. These conditions are weaker than those provided by Hu et al. (2008)

Strong consistencies of the bootstrap moments

Let X be a real valued random variable with E|X|r+δ<∞ for some positive integer r and real number, δ, 0<δ≤r, and let {X,X1,X2,…} be a sequence of independent, identically distributed random variables. In this note, we prove that, for almost all w∈Ω, μr;n*(w)→μr with probability 1. if limn→∞infm(n)n−β>0 for some β>r−δr+δ, where μr;n* is the bootstrap rth sample moment of the bootstrap sample some with sample size m(n) from the data set {X,X1,…,Xn} and μr is the rth moment of X. The results obtained here not only improve on those of Athreya [3] but also the proof is more elementary

Limiting behaviour of moving average processes under ρ\rho-mixing assumption

Let \{Y_i, -\infty<i<\infty\} be a doubly infinite sequence of identically distributed $\rho$-mixing random variables, \{a_i,-\infty<i< \infty\} an absolutely summable sequence of real numbers. In this paper, we prove the complete convergence and Marcinkiewicz-Zygmund strong law of large numbers for the partial sums of the moving average processes $\{\sum\limits^\infty_{i=-\infty}a_i Y_{i+n},n\geq1\}$

Convergence rate of the dependent bootstrapped means

In this paper, a Baum–Katz, Erdos, Hsu–Robbins, Spitzer type complete convergence result is obtained for the dependent bootstrapped means.National Sciences and Engineering Research Council of Canad

On complete convergence for arrays of rowwise independent random elements

A complete convergence theorem for arrays of rowwise independent random variables was proved by Sung, Volodin, and Hu. In this paper, we extend this theorem to the Banach space without any geometric assumptions on the underlying Banach space. Our theorem also improves some known results from the literature.Korea Research Foundation Gran

On the strong law for arrays and for the bootstrap mean and variance

Chung type strong laws of large numbers are obtained for arrays of rowwise independent random variables under various moment conditions. An interesting application of these results is the consistency of the bootstrap mean and variance

On convergence properties of sums of dependent random variables under second moment and covariance restrictions

Abstract For a sequence of dependent square-integrable random variables and a sequence of positive constants {b n , n ≥ 1}, conditions are provided under which the series n i=1 (X i − E X i )/b i converges almost surely as n → ∞ and {X n , n ≥ 1} obeys the strong law of large numbers lim n→∞ n i=1 (X i − E X i )/b n = 0 almost surely. The hypotheses stipulate that two series converge, where the convergence of the first series involves the growth rates of {Var X n , n ≥ 1} and {b n , n ≥ 1} and the convergence of the second series involves the growth rate of {sup n≥1 |Cov (X n , X n+k )|, k ≥ 1}

Operator Fractional Brownian Motion and Martingale Differences

It is well known that martingale difference sequences are very useful in applications and theory. On the other hand, the operator fractional Brownian motion as an extension of the well-known fractional Brownian motion also plays an important role in both applications and theory. In this paper, we study the relation between them. We construct an approximation sequence of operator fractional Brownian motion based on a martingale difference sequence

An online variational inference and ensemble based multi-label classifier for data streams.

Recently, multi-label classification algorithms have been increasingly required by a diversity of applications, such as text categorization, web, and social media mining. In particular, these applications often have streams of data coming continuously, and require learning and predicting done on-the-fly. In this paper, we introduce a scalable online variational inference based ensemble method for classifying multi-label data, where random projections are used to create the ensemble system. As a second-order generative method, the proposed classifier can effectively exploit the underlying structure of the data during learning. Experiments on several real-world datasets demonstrate the superior performance of our new method over several well-known methods in the literature

Satellite RNAs and Satellite Viruses of Plants

The view that satellite RNAs (satRNAs) and satellite viruses are purely molecular parasites of their cognate helper viruses has changed. The molecular mechanisms underlying the synergistic and/or antagonistic interactions among satRNAs/satellite viruses, helper viruses, and host plants are beginning to be comprehended. This review aims to summarize the recent achievements in basic and practical research, with special emphasis on the involvement of RNA silencing mechanisms in the pathogenicity, population dynamics, and, possibly, the origin(s) of these subviral agents. With further research following current trends, the comprehensive understanding of satRNAs and satellite viruses could lead to new insights into the trilateral interactions among host plants, viruses, and satellites