A Unified Theory of Empirical Likelihood Ratio Confidence Intervals for Survey Data with Unequal Probabilities

• Activity Number: 669
• Type: Contributed
• Date/Time: Thursday, August 2, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Section on Survey Research Methods
• Author(s): Yves Berger*+ and Omar De La riva Torres
• Companies: University of Southampton and University of Southampton
• Keywords: Design-based approach ; Stratification ; Unequal inclusion probabilities ; Consistency

Abstract

Standard confidence intervals based upon a normal distribution can perform poorly when the sampling distribution is not normal. EL confidence intervals may be better in this situation, as EL confidence intervals are determined by the distribution of the data (Rao & Wu 2009). The range of the parameter space is also preserved. This may not be the case for standard confidence intervals based upon a normal distribution, as standard confidence intervals can have negative lower bounds for a positive point estimator. Chen and Sitter (1999) proposed a pseudo EL approach which can be used to construct confidence intervals for the Hájek (1971) ratio estimator (Wu & Rao, 2006). The pseudo EL approach is not entirely appealing (Rao & Wu 2009) as it is not a genuine EL approach, it is not applicable to the Horvitz-Thompson (1952) estimator, and is limited to small sampling fraction. We propose a nov