A Strong Limit Theorem for Weighted Sums of Sequences of Negatively Dependent Random Variables

By Qunying Wu. 2010

50 citations recorded by the source corpus.

Applying the moment inequality of negatively dependent random variables which was obtained by Asadian et al. (2006), the strong limit theorem for weighted sums of sequences of negatively dependent random variables is discussed. As a result, the strong limit theorem for negatively dependent sequences of random variables is extended. Our results extend and improve the corresponding results of Bai and Cheng (2000) from the i.i.d. case to ND sequences.

Subfields: Demography, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/a6fbdc9a9076ec668122de86dc0c97664040a2e2

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In Demography

1. Aiting Shen
2. Shuhe Hu
3. Xuejun Wang
4. P. Chen
5. Chen Xu
6. D. Qiu
7. Tien-Chung Hu
8. Andrei Volodin

In Management Science and Operations Research

1. Aiting Shen
2. Shuhe Hu
3. Xuejun Wang
4. Andrei Volodin
5. Chen Xu
6. Lulu Zheng
7. Tien-Chung Hu
8. P. Chen

In Statistics and Probability

1. Aiting Shen
2. Shuhe Hu
3. Xuejun Wang
4. Chen Xu
5. Andrei Volodin
6. Lulu Zheng
7. Tien-Chung Hu
8. P. Chen

Citations in the corpus

• On complete convergence for widely orthant-dependent random variables and its applications in nonparametric regression models (2014, methodology): “For more details about NOD random variables, one can refer to Wang et al. (2010, 2011a, b), Wu (2006, 2010), Wu and Jiang (2011), Sung (2011), Qiu et al. (2011), and so forth.”
• Complete consistency for the estimator of nonparametric regression models based on extended negatively dependent errors (2015, background): “For the proof, one can refer to Wu, [30,31] Shen [32] or Shen and Wu.”
• Bernstein-Type Inequality for Widely Dependent Sequence and Its Application to Nonparametric Regression Models (2013, background): “[24–26], Wu [27, 28], Wu and Jiang [29], or Wu and Chen [30]).”
• Complete and complete moment convergence for weighted sums of widely orthant dependent random variables (2014, background): “They are called negatively orthant dependent (NOD) if they are both NUOD and NLOD (see, Block and Savits [1], Ebrahimi and Ghosh [6], Sung [19], Wu [25], Zarei and Jabbari [27]).”