Strong Limit Theorems for Weighted Sums of Nod Sequence and Exponential Inequalities

Abstract

Abstract. Some properties for negatively orthant dependent sequence are discussed. Some strong limit results for the weighted sums are obtained, which generalize the corresponding results for independent sequence and negatively associated sequence. At last, exponential inequalities for negatively orthant dependent sequence are presented.

Bernstein-Type Inequality for Widely Dependent Sequence and Its Application to Nonparametric Regression Models

“…Recall that when ( ) = ( ) = 1 for any ≥ 1 in 3and 4, the random variables { , ≥ 1} are called negatively upper orthant dependent (NUOD) and negatively lower orthant dependent (NLOD), respectively. If they are both NUOD and NLOD, then we say that the random variables { , ≥ 1} are negatively orthant dependent (NOD) (see, e.g., Ebrahimi and Ghosh [21], Block et al [22], Joag-Dev and Proschan [23], Wang et al [24][25][26], Wu [27,28], Wu and Jiang [29], or Wu and Chen [30]).…”

Limiting behaviour for arrays of row-wise END random variables under conditions of h-integrability

“…We can refer the reader to Taylor et al [15], Volodin [16], Amini and Bozorgnia [1], Ko and Kim [9], Ko et al [8], Volodin et al [17], Gan and Chen [5], Wu [19], Wu and Zhu [23], Qiu et al [12], Wang et al [18] and Wu et al [22]. However, according to our knowledge, except for Liu [10], Chen et al [2], Wu and Guan [21] and Qiu et al [13], few authors discussed the probabilistic properties for END random variables.…”

On Strong Convergence for Weighted Sums of a Class of Random Variables

“…Let { , , ≥ 1} be a sequence of identically distributed random variables and { ,1 ≤ ≤ , ≥ 1} an array of constants. The strong convergence results for weighted sums ∑ =1 have been studied by many authors; see, for example, Choi and Sung [1], Cuzick [2], Wu [3], Bai and Cheng [4], Chen and Gan [5], Cai [6], Sung [7,8], Shen [9], Wang et al [10][11][12][13][14], Zhou et al [15], Wu [16][17][18], Xu and Tang [19], and so forth. Many useful linear statistics are these weighted sums.…”