Bernstein-Type Inequality for Widely Dependent Sequence and Its Application to Nonparametric Regression Models

By Aiting Shen. 2013

79 citations recorded by the source corpus.

We present the Bernstein-type inequality for widely dependent random variables. By using the Bernstein-type inequality and the truncated method, we further study the strong consistency of estimator of fixed design regression model under widely dependent random variables, which generalizes the corresponding one of independent random variables. As an application, the strong consistency for the nearest neighbor estimator is obtained.

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

View Paper: https://www.semanticscholar.org/paper/a6a8968ac94a6cee8cb2c904d6cc11798b8682b4

How researchers see this paper

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

In Finance

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

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

• Complete consistency for the estimator of nonparametric regression models based on extended negatively dependent errors (2015, methodology): “Shen [28] presented the Bernstein-type inequality for widely dependent sequence and gave its applications to nonparametric regression models.”
• On complete convergence for widely orthant-dependent random variables and its applications in nonparametric regression models (2014, background): “The concept of general extended negative dependence was proposed by Liu (2009), Liu (2010) and further promoted by Chen et al. (2010), Chen et al. (2011), Shen (2011), Shen (2013a), Wang and Cheng (2011), Wang and Wang (2012), and so forth.”
• Exponential probability inequalities for WNOD random variables and their applications (2016, background): “1, we can get the following corollary immediately, which has been obtained by Shen [19].”