Properties of Chromy's sampling procedure

TL;DR

This paper analyzes Chromy's unequal probability sampling method, proving its statistical properties and providing formulas for variance estimation, which enhances understanding and application in survey sampling.

Contribution

It offers a theoretical analysis of Chromy's sampling procedure, including asymptotic normality and explicit second-order inclusion probabilities.

Findings

Horvitz-Thompson estimator is asymptotically normal

Explicit second-order inclusion probabilities derived

Variance can be unbiasedly estimated for the method

Abstract

Chromy (1979) proposed a unequal probability sampling algorithm, which enables to select a sample in one pass of the sampling frame only. This is the default sequential method used in the SURVEYSELECT procedure of the SAS software. In this article, we study the properties of Chromy sampling. We prove that the Horvitz-Thompson is asymptotically normally distributed, and give an explicit expression for the second-order inclusion probabilities. This makes it possible to estimate the variance unbiasedly for the randomized version of the method programmed in the SURVEYSELECT procedure.