Table of Contents
ISRN Biomathematics
Volume 2013 (2013), Article ID 765752, 8 pages
http://dx.doi.org/10.1155/2013/765752
Research Article

Confidence Intervals for the Mean Based on Exponential Type Inequalities and Empirical Likelihood

1Faculty of Physics and Mathematics, University of Latvia, Zellu Street 8, Riga, LV-1002, Latvia
2Department of Biostatistics, Bioinformatics, and Biomathematics, Georgetown University, Suite 180, Building D, 4000 Reservoir Rd., NW, Washington, DC 20057-1484, USA

Received 17 July 2013; Accepted 19 September 2013

Academic Editors: J. Fellman and O. François

Copyright © 2013 Sandra Vucane et al. 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

For independent observations, recently, it has been proposed to construct the confidence intervals for the mean using exponential type inequalities. Although this method requires much weaker assumptions than those required by the classical methods, the resulting intervals are usually too large. Still in special cases, one can find some advantage of using bounded and unbounded Bernstein inequalities. In this paper, we discuss the applicability of this approach for dependent data. Moreover, we propose to use the empirical likelihood method both in the case of independent and dependent observations for inference regarding the mean. The advantage of empirical likelihood is its Bartlett correctability and a rather simple extension to the dependent case. Finally, we provide some simulation results comparing these methods with respect to their empirical coverage accuracy and average interval length. At the end, we apply the above described methods for the serial analysis of a gene expression (SAGE) data example.