Large sample properties of the Midzuno sampling scheme with probabilities proportional to size

TL;DR

This paper investigates the statistical properties of Midzuno sampling, proving its asymptotic normality and proposing consistent variance estimators to improve ratio estimation accuracy.

Contribution

It provides the first rigorous proof of asymptotic normality for Midzuno sampling estimators and introduces consistent variance estimators.

Findings

Asymptotic normality of estimators established

Consistent variance estimators proposed

Enhanced ratio estimation accuracy

Abstract

Midzuno sampling enables to estimate ratios unbiasedly. We prove the asymptotic normality for estimators of totals and ratios under Midzuno sampling. We also propose consistent variance estimators.