Finite population inference for skewness measures

In this article we consider Bowley’s skewness measure and the Groeneveld-Meeden b3 index in the context of finite population sampling. We employ the functional delta method to obtain asymptotic variance formulae for plug-in estimators and propose corresponding variance estimators. We then consider plug-in estimators based on the Ha´jek cdf-estimator and on a Deville-Sa¨rndal type calibration estimator and test the efficiency of the corresponding variance estimators and normal confidence intervals in a simulation study.