Complete convergence for arrays of rowwise negatively superadditive-dependent random variables and its applications

Wang, Xuejun; Deng, Xin; Zheng, Lulu; Hu, Shuhe

doi:10.1080/02331888.2013.800066

Cited by 79 publications

(31 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As pointed out and proved by Joag-Dev and Proschan (1983), a number of well-known multivariate distributions possess the NA property, such as multinomial, convolution of unlike multionmial, multivariate hypergeometric, Dirichlet, permutation distribution, negatively correlated normal distribution, random sampling without replacement and joint distribution of ranks. For more details about NA random variables, one can refer to Matula (1992), Shao (2000), Chen et al (2008), Ling (2008), Liang and Zhang (2010), Sung (2011), Zarei and Jabbari (2011), Hu (2012, 2014), Wang et al (2011Wang et al ( , 2014a, and so on.…”

Section: Introductionmentioning

confidence: 99%

Moment inequalities for m-negatively associated random variables and their applications

et al. 2015

View full text Add to dashboard Cite

The moment inequalities for m-NA random variables, especially the Marcinkiewicz-Zygmund type inequality and Rosenthal type inequality are established and the Khintchine-Kolmogorov convergence theorem and the three series theorem for m-NA random variables are also obtained. As one application of the moment inequalities, we study the large deviation for least squares estimator in nonlinear regression models under some general conditions. As another application, we investigate the strong consistency for least squares estimator in multiple linear regression models based on m-NA random variables.Keywords m-Negatively associated random variables · Marcinkiewicz-Zygmund type inequality · Rosenthal type inequality · Nonlinear regression models · Multiple linear regression models Mathematics Subject Classification 60E05 · 60F15 · 62J02 · 62J05 · 62F12

show abstract

Section: Introductionmentioning

confidence: 99%

Moment inequalities for m-negatively associated random variables and their applications

et al. 2015

View full text Add to dashboard Cite

show abstract

“…Similarly to the proof of Theorem 2 of Shao ( [15]) and by using Lemma 2.2, Wang et al ( [25]) got the following Rosenthal-type maximal inequality for NSD random variables. Lemma 2.3.…”

Section: Preliminary Lemmasmentioning

confidence: 99%

Strong Convergence for weighed sums of negatively superadditive dependent random variables

Chen¹,

Wang²,

Wang³

et al. 2016

Kybernetika

Self Cite

View full text Add to dashboard Cite

“…Shen et al [14] established the strong limit theorems for NSD random variables. Wang et al [20] investigated the complete convergence for arrays of rowwise NSD random variables and gave its applications to nonparametric regression model. Shen et al [17] obtained some strong convergence properties for weighted sums of NSD random variables.…”

Section: Introductionmentioning

confidence: 99%

Complete moment convergence and complete convergence for weighted sums of NSD random variables

Deng

Wang

et al. 2015

RACSAM

Self Cite

View full text Add to dashboard Cite

In this paper, the equivalent conditions of complete moment convergence of the maximum partial weighted sums for negatively superadditive dependent (NSD) random variables are established without the assumption of identical distribution. As applications, the complete moment convergence, the complete convergence and strong law of large numbers for NSD random variables are obtained. The results obtained in the paper generalize or improve the corresponding ones for weighted sums of independent random variables and negatively associated random variables.

show abstract

Complete convergence for arrays of rowwise negatively superadditive-dependent random variables and its applications

Cited by 79 publications

References 26 publications

Moment inequalities for m-negatively associated random variables and their applications

Moment inequalities for m-negatively associated random variables and their applications

Strong Convergence for weighed sums of negatively superadditive dependent random variables

Complete moment convergence and complete convergence for weighted sums of NSD random variables

Contact Info

Product

Resources

About