Probability inequalities for END sequence and their applications

By Aiting Shen. 2011

98 citations recorded by the source corpus.

Some probability inequalities for extended negatively dependent (END) sequence are provided. Using the probability inequalities, we present some moment inequalities, especially the Rosenthal-type inequality for END sequence. At last, we study the asymptotic approximation of inverse moment for nonnegative END sequence with finite first moments, which generalizes and improves the corresponding results of Wu et al. [Stat. Probab. Lett. 79, 1366-1371 (2009)], Wang et al. [Stat. Probab. Lett. 80, 452-461 (2010)], and Sung [J. Inequal. Appl. 2010, Article ID 823767, 13pp. (2010). doi:10.1155/2010/823767].MSC(2000): 60E15; 62G20.

Subfields: Artificial Intelligence, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/74838e14cf0de6b955dc8733a0b40b48b6510b5e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

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

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. Mei Yao
8. Wenjuan Wang

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. Mei Yao

Citations in the corpus

• On complete convergence for widely orthant-dependent random variables and its applications in nonparametric regression models (2014, methodology): “Inspired by Fakoor and Azarnoosh (2005), Asadian et al. (2006) and Shen (2011), we can get the following probability inequality for WOD random variables.”
• Bernstein-Type Inequality for Widely Dependent Sequence and Its Application to Nonparametric Regression Models (2013, unknown): “[26] X. J.Wang, S.H.Hu,A. T. Shen, andW.”
• On Complete Convergence for an Extended Negatively Dependent Sequence (2014, background): “1 below has been proved by Shen (2011) and the second inequality of Lemma 2.1 can be proved by a similar way of Theorem 2.3.1 in Stout (1974). So we omit the details of the proof.”
• Complete consistency for the estimator of nonparametric regression models based on extended negatively dependent errors (2015, background): “Shen [7] presented some probability inequalities for END sequences and gave some applications.”
• Complete convergence for weighted sums of END random variables and its application to nonparametric regression models (2016, methodology): “For more details about END random variables, one can refer to Chen, Chen, and Ng (2010), Shen (2011), Wu and Guan (2012), Wang and Wang (2013), Qiu, Chen, Antonini, and Volodin (2013), Wang, Hu, Volodin, and Hu (2013a), Wang, Wang, Hu, Ling, and Wei (2013b), Wang, Zheng, Xu, and Hu (2015), Hu,…”
• Exponential probability inequalities for WNOD random variables and their applications (2016, background): “There are only some literatures studying the probability limiting behavior of WNOD random variables, such as Wang et al. [23], Wang and Cheng [34], Wang et al. [35], Liu et al. [10], Chen et al. [4], Shen [19], Qiu and Chen [12], Qiu and Hu [14], Wang et al. [31], Yang et al. [43], and so on.”