Confidence intervals for nonparametric regression functions under negatively associated errors

Abstract

In this paper, we study the construction of confidence intervals for a nonparametric regression function under a negatively associated sample by using the blockwise technique. It is shown that the blockwise empirical likelihood (EL) ratio statistic is asymptotically χ² distributed. The result is used to obtain EL-based confidence intervals for a nonparametric regression function. The results of a simulation study on the finite sample performance of the proposed confidence intervals are reported.

Keywords:

• negatively associated sample
• nonparametric regression
• empirical likelihood
• confidence interval

AMS 2000 Subject Classifications:

• Primary: 62G05
• Secondary: 62E20

Acknowledgements

This work was partially supported by the National Natural Science Foundation of China (10971038), the Natural Science Foundation of Guangxi (2010 GXNSFA 013117), the Program for Excellent Talents in Guangxi Higher Education Institutions, and the New Century Ten, Hundred and Thousand Talents Project of Guangxi. The authors are thankful to two referees, an associate editor, and an editor for constructive suggestions.