Finite-Sample Properties of Adjusted Empirical Likelihood

• Activity Number: 462
• Type: Contributed
• Date/Time: Wednesday, August 1, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Yi Huang*+ and Jiahua Chen
• Companies: University of British Columbia and SSC
• Keywords: Adjusted Empirical Likelihood ; Confidence Regions ; Finite-Sample Prperties ; High-Order Precision

Abstract

In this talk we present several interesting finite-sample properties of the adjusted empirical likelihood (AEL). The AEL ratio function increases when the putative population mean moves away from the sample mean. Thus, the AEL confidence region of the population mean is star-shaped. The AEL ratio function decreases when the level of adjustment increases. Hence, its coverage probability increases with the level of adjustment. Finally, the AEL ratio function is always bounded, leading to unbounded confidence regions when the sample size is small and/or the nominal confidence level is high. We discover that linking the level of adjustment with the putative population mean ensures bounded confidence regions and preserves the asymptotic properties.