Bootstrap procedures for the pseudo empirical likelihood method in sample surveys

Pseudo empirical likelihood ratio confidence intervals for finite population parameters are based on asymptotic χ2χ2 approximation to an adjusted pseudo empirical likelihood ratio statistic, with the adjustment factor related to the design effect. The calculation of the design effect involves variance estimation and hence requires second order inclusion probabilities. It also depends on how auxiliary information is used, and needs to be derived one-at-a-time for different scenarios. This paper presents bootstrap procedures for constructing pseudo empirical likelihood ratio confidence intervals. The proposed method bypasses the need for design effects and is valid under general single-stage unequal probability sampling designs with small sampling fractions. Different scenarios in using auxiliary information are handled by simply including the same type of benchmark constraints with the bootstrap procedures. Simulation results show that the bootstrap calibrated intervals perform very well and have much improved coverage probabilities over the χ2χ2-based intervals when the sample sizes are small or moderate.