Empirical Likelihood Confidence Intervals under the Rao-Hartley-Cochran Sampling Design

• Activity Number: 405
• Type: Contributed
• Date/Time: Tuesday, August 5, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Survey Research Methods Section
• Author(s): Yves Berger and Melike Oguz Alper*+
• Companies: University of Southampton and University of Southampton
• Keywords: Design-based inference ; estimating equations ; empirical likelihood ; stratification ; unequal inclusion probabilities

Abstract

The Hartley-Rao-Cochran ( RHC ) sampling design (Rao et al., 1962) is a popular unequal probability sampling design. We show how empirical likelihood confidence intervals can be derived under this sampling design. Berger and De La Riva Torres (2012) proposed an empirical likelihood approach which can be used for point estimation and to construct confidence intervals under complex sampling designs. We show how this approach can be adjusted for the RHC sampling design. The proposed approach intrinsically incorporates sampling weights and auxiliary information. It may give better coverages than standard methods even when the sampling distribution of the parameters of interest is not normal. The proposed approach is simple to implement and less computer intensive than bootstrap. The proposed approach does not rely on re-sampling, linearisation, variance estimation, or design-effects.