A comparison of pivotal sampling and unequal probability sampling with replacement

TL;DR

This paper demonstrates that pivotal sampling is more efficient than multinomial sampling, ensuring better estimator properties and supported by simulation results.

Contribution

It proves the efficiency of pivotal sampling over multinomial sampling and establishes related estimator properties.

Findings

Pivotal sampling is more efficient than multinomial sampling.

Horvitz-Thompson estimator is weakly consistent under pivotal sampling.

Simulation studies support the theoretical results.

Abstract

We prove that any implementation of pivotal sampling is more efficient than multinomial sampling. This property entails the weak consistency of the Horvitz-Thompson estimator and the existence of a conservative variance estimator. A small simulation study supports our findings.