On complete moment convergence for nonstationary negatively associated random variables

Abstract

The purpose of this paper is to establish the complete moment convergence for nonstationary negatively associated random variables satisfying the weak mean domination condition. The result is an improvement of complete convergence in Marcinkiewicz-Zygmund-type SLLN for negatively associated random variables in

Complete Moment Convergence for Arrays of Rowwise Negatively Associated Random Variables and Its Application in Non-Parametric Regression Model

“…The results obtained in this paper correct the result obtained in Ko [13] and also improve and extend Theorems A and B for NA random variables. The meaningful case αp = 1 that was not considered in either Kuczmaszewska [14] or Ko [13] is also considered in this paper. It is worth mentioning that the proof of our main results is different from that of Ko [13].…”

“…The results obtained in this paper correct the corresponding one obtained in Ko [13] and also improve and generalize the corresponding ones of Kuczmaszewska [14] and Ko [13]. As an application of the main results, we present a result on complete consistency for the estimator in a non-parametric regression model based on NA errors.…”

“…In Theorem 3.1, we not only present the result in the case 0 < p ≤ 1, but also improve the corresponding one of Ko [13] in the case p > 1. Moreover, the proof is different from that of Ko [13]. The main improvements and difference are listed below.…”

“…The meaningful case αp = 1 that was not considered in either Kuczmaszewska [14] or Ko [13] is also considered in this paper. It is worth mentioning that the proof of our main results is different from that of Ko [13]. As an application of our main results, we present a result on complete consistency for the estimator in a non-parametric regression model based on NA errors.…”

“…(iii) for the case p > 1, the exponent r is improved from r ≡ 1 to any 0 < r < p; (iv) Ko [13] mainly adopted the formula E|X| = ∞ 0 P (|X| > t)dt and the truncation method, by which the result in the case 0 < p ≤ 1 can hardly be obtained. However, in this paper, we establish a general moment inequality (see Lemma 2.2), and by utilizing the inequality, we easily obtain a much more general result only by some standard discussions.…”