Pingyan Chen

ON THE COMPLETE CONVERGENCE FOR ARRAYS OF ROWWISE EXTENDED NEGATIVELY DEPENDENT RANDOM VARIABLES

Abstract. A general result for the complete convergence of arrays ofrowwise extended negatively dependent random variables is derived. Asits applications eight corollaries for complete convergence of weightedsums for arrays of rowwise extended negatively dependent random vari-ables are given, which extend the corresponding known results for inde-pendent case. 1. IntroductionThe concept of complete convergence of a sequence of random variables wasintroduced by Hsu and Robbins ([5]) as follows. A sequence {U n ,n≥ 1} ofrandom variables converges completely to the constant θifX ∞n=1 P{|U n −θ| >ǫ} 0.Moreover, they proved that the sequence of arithmetic means of independentidentically distribution (i.i.d.) random variables converges completely to theexpected value if the variance of the summands is finite. This result has beengeneralized and extended in several directions, see Gut ([3], [4]), Hu et al. ([7],[8]), Chen et al. ([2]), Sung ([14], [15], [17]), Zarei and Jabbari ([20]), Baek etal. ([1]). In particular, Sung ([14]) obtained the following two Theorems A andB.Theorem A. Let {X

ON COMPLETE CONVERGENCE FOR ARRAYS OF ROW-WISE NEGATIVELY ASSOCIATED RANDOM VARIABLES

We obtain a complete convergence result for arrays of row-wise negatively associated random variables which extends the results of Hu, Szynal, and Volodin [Statist. Probab. Lett., 38 (1998), pp. 27–31], Hu et al. [Commun. Korean Math. Soc., 18 (2003), pp. 375–383], and Sung, Volodin, and Hu [Statist. Probab. Lett., 71 (2005), pp. 303–311] by the methods developed by Kruglov, Volodin, and Hu [Statist. Probab. Lett., 76 (2006), pp. 1631–1640].

Limiting behaviour of moving average processes under negative association assumption

Let {Yi,−∞ < i < ∞} be a doubly infinite sequence of identically distributed negatively associated random variables, and {ai,−∞ < i < ∞} an absolutely summable sequence of real numbers. In this paper, we prove the complete convergence and complete moment convergence of the maximum partial sums of moving average processes {∑∞ i=−∞ aiYi+n, n ≥ 1 } . We improve the results of Baek et al. (2003) and Li and Zhang (2005).

Complete moment convergence for weighted sums of extended negatively dependent random variables

ABSTRACT Complete moment convergence for weighted sums of sequence of extended negatively dependent (END) random variables is discussed. Some new sufficient and necessary conditions of complete moment convergence for weighted sums of END random variables are obtained, which improve and extend some well-known results in the literature.

L 1-Convergence for Weighted Sums of Some Dependent Random Variables

In this article, the authors discuss the L 1-convergence for weighted sums of some dependent random variables under the condition of h-integrability with respect to an array of weights. The dependence structure of the random variables includes pairwise lower case negative dependence and conditions on the mixing coefficient, the maximal correlation coefficient, or the ρ*-mixing coefficient. They prove that all the weighted sums have similar limiting behaviour.

Strong Laws for Certain Types of U-statistics Based on Negatively Associated Random Variables

We establish the Marcinkiewicz-Zygmund-type strong laws of large numbers for certain class of multilinear U-statistics based on negatively associated random variables.

A Note on Complete Convergence for Arrays of Rowwise Independent Banach Space Valued Random Elements

We obtain complete convergence results for arrays of rowwise independent Banach space valued random elements. Compared with similar results presented in the probabilistic literature our conditions are weaker.

On complete convergence and complete moment convergence for weighted sums of \(\rho^{*}\)-mixing random variables

AbstractLet r≥1

Complete convergence for weighted sums of i.i.d. random variables with applications in regression estimation and EV model

r\geq1

Generalized Law of the Iterated Logarithm and Its Convergence Rate

, 1≤p<2