Back To Index Previous Article Next Article Full Text


Statistica Sinica 21 (2011), 1767-1783
doi:10.5705/ss.2009.117





CONSTRUCTING NONPARAMETRIC LIKELIHOOD

CONFIDENCE REGIONS WITH HIGH ORDER PRECISIONS


Xiao Li$^{1}$, Jiahua Chen$^{2}$, Yaohua Wu$^{1}$ and Dongsheng Tu$^{3}$


$^1$University of Science and Technology of China,
$^2$University of British Columbia and $^3$Queen's University$^{3}$


Abstract: Empirical likelihood is a natural tool for nonparametric statistical inference, and a member of nonparametric likelihoods. Inferences based on this class of likelihoods have the same first order asymptotic properties. One member of the class, exponential tilting likelihood, has been found to be stable to model mis-specification but is not as efficient as empirical likelihood. Exponentially tilted empirical likelihood, also called exponential empirical likelihood, was proposed to achieve both stability and efficiency. Unlike empirical likelihood, however, the hybrid likelihood is not Bartlett correctable, and the precision of its confidence regions is compromised when the sample size is not large. We introduce a novel adjustment procedure and show that it attains the high order precision that is not attained by the usual Bartlett correction. Simulation results confirm the improved precision in coverage probabilities.



Key words and phrases: Bartlett correction, edgeworth expansion, empirical likelihood, estimating equation, exponential empirical likelihood, exponential tilting, Wilks' theorem.

Back To Index Previous Article Next Article Full Text