Laws of large numbers for Cesàro alpha-integrable random variables under dependence condition AANA or AQSI

Abstract

Both residual Cesàro alpha-integrability (RCI(α)) and strongly residual Cesàro alphaintegrability (SRCI(α)) are two special kinds of extensions to uniform integrability, and both asymptotically almost negative association (AANA) and asymptotically quadrant sub-independence (AQSI) are two special kinds of dependence structures. By relating the RCI(α) property as well as the SRCI(α) property with dependence condition AANA or AQSI, we formulate some tail-integrability conditions under which for appropriate α the RCI(α) property yields L1-convergence results and the SRCI(α) property yields strong laws of large numbers, which is the continuation of the corresponding literature.

On the strong convergence for weighted sums of asymptotically almost negatively associated random variables

“…For example, Chandra and Ghosal [4], Wang et al [17], Ko et al [6], Yuan and An [22,23], Yuan and Wu [24], Wang et al [13,14,15], Yang et al [18], Hu et al [5], Shen and Wu [7], Tang [10], and so forth. Hence, it is very significant to study limit properties of this wider AANA random variables in probability theory and practical applications.…”

On Consistency of the Nearest Neighbor Estimator of the Density Function for m-AANA Samples

“…Since the concept of AANA random variables was put forward by Chandra and Ghosal [9], plenty of results have been established concerning this dependence structure. For instance, Kim and Ko [10] developed the Hajeck-Renyi inequality for these dependent random variables; Yuan and An [11] established some moment inequalities for maximum sums; Chandra and Ghosal [12] as well as Shen and Wu [13] proved the strong law of large numbers for weighted sums; Yuan and An [14] investigated the laws of large numbers for this dependent random variables satisfying the Cesàro alpha-integrability condition; and Wu and Wang [15] studied some results on the nearest neighbor estimator of the density function under AANA samples.…”

Complete convergence and complete moment convergence for arrays of rowwise asymptotically almost negatively associated random variables

“…Since the concept of AANA was introduced by Chandra and Ghosal [4], many applications have been established in various aspects. For more details, we can refer to Chandra and Ghosal [4,5], Ko et al [6], Yuan and An [7,8] , Yuan and Wu [9], Wang et al [10][11][12], Yang et al [13], Hu et al [14], Tang [15], Shen and Wu [16], Huang et al [17], Shen et al [18], and so forth.…”