Finite-sample properties of the adjusted empirical likelihood

Abstract

Empirical likelihood-based confidence intervals for the population mean have many interesting properties [Owen, A.B. (1988), ‘Empirical Likelihood Ratio Confidence Intervals for a Single Functional’, Biometrika, 75, 237–249]. Calibrated by χ² limiting distribution, however, their coverage probabilities are often lower than the nominal when the sample size is small and/or the dimension of the data is high. The application of adjusted empirical likelihood (AEL) is one of the many ways to achieve a more accurate coverage probability. In this paper, we study the finite-sample properties of the AEL. We find that the AEL ratio function decreases when the level of adjustment increases. Thus, the AEL confidence region has higher coverage probabilities when the level of adjustment increases. We also prove that the AEL ratio function increases when the putative population mean moves away from the sample mean. In addition, we show that the AEL confidence region for the population mean is convex. Finally, computer simulations are conducted to further investigate the precision of the coverage probabilities and the sizes of the confidence regions. An application example is also included.

Keywords:

• confidence region
• convexity
• coverage probability
• high-order precision
• pseudo-point

AMS Subject Classification: :

• 62G15

Acknowledgements

The authors thank the editor and three anonymous referees for their insightful comments and suggestions on this paper, which have led to significant improvements.