School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA. e-mail: firstname.lastname@example.org
EMPIRICAL LIKELIHOOD METHODS FOR THE GINI INDEX
Article first published online: 11 JUL 2011
© 2011 Australian Statistical Publishing Association Inc.
Australian & New Zealand Journal of Statistics
Volume 53, Issue 2, pages 131–139, June 2011
How to Cite
Peng, L. (2011), EMPIRICAL LIKELIHOOD METHODS FOR THE GINI INDEX. Australian & New Zealand Journal of Statistics, 53: 131–139. doi: 10.1111/j.1467-842X.2011.00614.x
- Issue published online: 20 OCT 2011
- Article first published online: 11 JUL 2011
- empirical likelihood;
- Gini index
The Gini index and its generalizations have been used extensively for measuring inequality and poverty in the social sciences. Recently, interval estimation based on nonparametric statistics has been proposed in the literature, for example the naive bootstrap method, the iterated bootstrap method and the bootstrap method via a pivotal statistic. In this paper, we propose empirical likelihood methods to construct confidence intervals for the Gini index or the difference of two Gini indices. Simulation studies show that the proposed empirical likelihood method performs slightly worse than the bootstrap method based on a pivotal statistic in terms of coverage accuracy, but it requires less computation. However, the bootstrap calibration of the empirical likelihood method performs better than the bootstrap method based on a pivotal statistic.