Some Limit Theorems for Sequences of Pairwise NQD Random Variables

doi:10.1016/S0252-9602(08)60027-2

Acta Mathematica Scientia

Volume 28, Issue 2, April 2008, Pages 269-281

https://doi.org/10.1016/S0252-9602(08)60027-2 Get rights and content

Abstract

In this article, the authors study some limit properties for sequences of pairwise NQD random variables, which are not necessarily identically distributed. They obtain Baum and Katz complete convergence and the strong stability of Jamison's weighted sums for pairwise NQD random variables, which may have different distributions. Some well-known results are improved and extended.

References (8)

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There are more references available in the full text version of this article.

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Asymptotic normality and mean consistency for the weighted estimator in nonparametric regression models
2019, Journal of the Korean Statistical Society
Citation Excerpt :
Substantial limit theorems for pairwise NQD random variables have been established. One can refer to Chen, Bai, and Sung (2014), Gan and Chen (2008), Mutula (1992), Wu (2002), Wang, Su, and Liu (1998) and Wang, Yang, Cheng, and Cai (2001) among others. Newman (1984) first formulated the notion of linearly negative quadrant dependent (LNQD, for short) as follows:
In this paper, we mainly study the asymptotic properties of weighted estimator for the nonparametric regression model based on linearly negative quadrant dependent (LNQD, for short) errors. We obtain the rate of uniformly asymptotic normality of the weighted estimator which is nearly $O (n^{- 1 ∕ 4})$ when the moment condition is appropriate. The results generalize the corresponding ones of Yang (2003) from NA samples to LNQD samples and improve or extend the corresponding one of Li et al. (2012) for LNQD samples. Moreover, we obtain some results on mean consistency, uniformly mean consistency, and the rate of mean consistency for the weighted estimator. Finally we carry out some simulations to verify the validity of our results.
Complete convergence and the strong laws of large numbers for pairwise NQD random variables
2019, Communications in Statistics - Theory and Methods
On complete moment convergence for arrays of rowwise pairwise negatively quadrant dependent random variables
2019, Journal of Inequalities and Applications
Complete q-th moment convergence and its application in the dependent bootstrap
2018, Stochastics
Baum–Katz type theorems with exact threshold
2018, Stochastics
The moment of maximum normed sums of randomly weighted pairwise nqd sequences
2018, Journal of Mathematical Inequalities

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: Supported by the National Natural Science Foundation of China (10671149)

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Some Limit Theorems for Sequences of Pairwise NQD Random Variables

Abstract

Statist Probab Lett

Convergence rates in the law of large numbers

Trans Amer Math Soc

Convergence of weighted averages of independent random variables

Z Wahrscheinlichkeitstheorie

Negative association of random variables with applications

Ann Statist