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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 862602, 9 pages
http://dx.doi.org/10.1155/2013/862602
Research Article

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

School of Mathematical Science, Anhui University, Hefei 230601, China

Received 8 February 2013; Accepted 2 July 2013

Academic Editor: Juan J. Trujillo

Copyright © 2013 Aiting Shen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Citations to this Article [9 citations]

The following is the list of published articles that have cited the current article.

  • Xuejun Wang, Meimei Ge, Shuhe Hu, and Xize Wang, “The Strong Consistency of the Estimator of Fixed-Design Regression Model under Negatively Dependent Sequences,” Abstract and Applied Analysis, vol. 2013, pp. 1–7, 2013. View at Publisher · View at Google Scholar
  • Xuejun Wang, Chen Xu, Tien-Chung Hu, Andrei Volodin, and Shuhe Hu, “On complete convergence for widely orthant-dependent random variables and its applications in nonparametric regression models,” Test, vol. 23, no. 3, pp. 607–629, 2014. View at Publisher · View at Google Scholar
  • Xin Deng, Meimei Ge, Xuejun Wang, Yanfang Liu, and Yu Zhou, “Complete Convergence for Weighted Sums of a Class of Random Variables,” Filomat, vol. 28, no. 3, pp. 509–522, 2014. View at Publisher · View at Google Scholar
  • Xuejun Wang, Yi Wu, and Shuhe Hu, “Exponential probability inequality for $$m$$ m -END random variables and its applications,” Metrika, vol. 79, no. 2, pp. 127–147, 2015. View at Publisher · View at Google Scholar
  • Xuejun Wang, and Shuhe Hu, “The consistency of the nearest neighbor estimator of the density function based on WOD samples,” Journal of Mathematical Analysis and Applications, 2015. View at Publisher · View at Google Scholar
  • Xuejun Wang, Lulu Zheng, Chen Xu, and Shuhe Hu, “Complete consistency for the estimator of nonparametric regression models based on extended negatively dependent errors,” Statistics, vol. 49, no. 2, pp. 396–407, 2015. View at Publisher · View at Google Scholar
  • Xufeng Huang, Xufei Tang, Xin Deng, and Xuejun Wang, “The large deviation for the least squares estimator of nonlinear regression model based on WOD errors,” Journal Of Inequalities And Applications, 2016. View at Publisher · View at Google Scholar
  • Zhiyong Chen, Haibin Wang, and Xuejun Wang, “The consistency for the estimator of nonparametric regression model based on martingale difference errors,” Statistical Papers, vol. 57, no. 2, pp. 451–469, 2016. View at Publisher · View at Google Scholar
  • Aiting Shen, Mei Yao, Wenjuan Wang, and Andrei Volodin, “Exponential probability inequalities for WNOD random variables and their applications,” Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-Matematicas, vol. 110, no. 1, pp. 251–268, 2016. View at Publisher · View at Google Scholar