Jackknife empirical likelihood with complex surveys

Abstract

We propose the so-called jackknife empirical likelihood approach for the survey data of general unequal probability sampling designs, and analyze parameters defined according to U-statistics. We prove theoretically that jackknife pseudo-empirical likelihood ratio statistic is asymptotically distributed as a chi-square random variable, and can be used to construct confidence intervals for complex survey samples. In the process of research, we consider with or without auxiliary information, utilizing design weights or calibration weights. Simulation studies are included to examine that in terms of coverage probability and tail error rates, the jackknife pseudo-empirical likelihood ratio confidence intervals are superior to those based on the normal approximation.