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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.

Abstract

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.