Finite population inference for skewness measures

TL;DR

This paper develops asymptotic variance formulas and confidence interval methods for Bowley's skewness and Groeneveld-Meeden's index in finite population sampling, enhancing statistical inference accuracy.

Contribution

It introduces new variance estimators and evaluates their performance for skewness measures using the functional delta method and calibration techniques.

Findings

Asymptotic variance formulas are derived for skewness estimators.

Calibration-based estimators improve confidence interval coverage.

Performance of normal confidence intervals is assessed in finite populations.

Abstract

In this article we consider Bowley's skewness measure and the Groeneveld-Meeden $b_{3}$ 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 H\'{a}jek cdf-estimator and on a Deville-S\"arndal type calibration estimator and test the performance of normal confidence intervals.