Limiting Behaviors of Weighted Sums for Linearly Negative Quadrant Dependent Random Variables

Ko, Mi-Hwa; Ryu, Dae-Hee; Kim, Taesung

doi:10.11650/twjm/1500404705

Cited by 17 publications

(7 citation statements)

References 11 publications

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“…Our third conditionally exponential type inequality generalizes Theorem 2.1 in Ko et al [7] from non-conditional case to conditional case. Theorem 3 Let {X n , n ≥ 1} be a sequence of F-centered and F-LNQD random vari-…”

Section: Lemma 1 For a Random Eventsupporting

confidence: 64%

Conditional limit theorems for conditionally linearly negative quadrant dependent random variables

Yuan

Xie

2012

Monatsh Math

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From the ordinary notion of linearly negative quadrant dependence for a sequence of random variables, a new concept called conditionally linearly negative quadrant dependence is introduced. The relation between the two kinds of dependence is answered by examples, that is, the linearly negative quadrant dependence does not imply the conditionally linearly negative quadrant dependence, and vice versa. The fundamental properties of conditionally linearly negative quadrant dependence are developed, which extend the corresponding ones under the non-conditioning setup. By means of these properties, some conditional exponential inequalities, conditionally complete convergence results and a conditional central limit theorem stated in terms of conditional characteristic functions are established.

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Section: Lemma 1 For a Random Eventsupporting

confidence: 64%

Conditional limit theorems for conditionally linearly negative quadrant dependent random variables

Yuan

Xie

2012

Monatsh Math

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“…[10] [12], this lemma is easily proved by following Fuk and Nagaev [13]. Here we omit the details of the proof.…”

Section: Preliminary Lemmasmentioning

confidence: 90%

Mean convergence theorems and weak laws of large numbers for weighted sums of dependent random variables

Guan

2011

Journal of Mathematical Analysis and Applications

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Under some conditions of uniform integrability and appropriate conditions, mean convergence theorems and weak laws of large numbers for weighted sums of dependent random variables are obtained. Our results extend and improve the results of [H.S. Sung, S. Lisawadi, A. Volodin, Weak laws of large numbers for arrays under a condition of uniform integrability, J. Korean Math. Soc. 45 (2008) 289-300] and [M. Ordóñez Cabrera, A. Volodin, Mean convergence theorems and weak laws of large numbers for weighted sums of random variables under a condition of weighted integrability, J. Math. Anal. Appl. 305 (2005) 644-658].

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“…Ko et al [2] obtained the Hoeffding-type inequality for LNQD sequence. Ko et al [3] studied the strong convergence for weighted sums of LNQD arrays, Wang et al [7] got the exponential inequalities and complete convergence for a LNQD sequence, Wu et al [9] studied the mean convergence and complete convergence for LNQD sequence, and so forth. It is easily seen that independent random variables and negatively associated (NA, in short) random variables are LNQD.…”

Section: Introductionmentioning

confidence: 99%

Complete convergence for weighted sums of LNQD random variables

Shen

Zhu

et al. 2014

Stochastics

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Limiting Behaviors of Weighted Sums for Linearly Negative Quadrant Dependent Random Variables

Cited by 17 publications

References 11 publications

Conditional limit theorems for conditionally linearly negative quadrant dependent random variables

Conditional limit theorems for conditionally linearly negative quadrant dependent random variables

Mean convergence theorems and weak laws of large numbers for weighted sums of dependent random variables

Complete convergence for weighted sums of LNQD random variables

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