A cautionary note on the Hanurav-Vijayan sampling algorithm

TL;DR

This paper critically examines the Hanurav-Vijayan sampling algorithm, revealing its equivalence to the Sunter procedure, its inconsistency with the Horvitz-Thompson estimator, and proposing a more reliable alternative.

Contribution

It proves the equivalence of Hanurav-Vijayan and Sunter procedures, demonstrates the estimator's inconsistency, and introduces a consistent conditional estimator as a replacement.

Findings

Hanurav-Vijayan is equivalent to Sunter procedure

Horvitz-Thompson estimator is not generally consistent

Proposed a conditional estimator with proven consistency

Abstract

We consider the Hanurav-Vijayan sampling design, which is the default method programmed in the SURVEYSELECT procedure of the SAS software. We prove that it is equivalent to the Sunter procedure, but is capable of handling any set of inclusion probabilities. We prove that the Horvitz-Thompson estimator is not generally consistent under this sampling design. We propose a conditional Horvitz-Thompson estimator, and prove its consistency under a non-standard assumption on the first-order inclusion probabilities. Since this assumption seems difficult to control in practice, we recommend not to use the Hanurav-Vijayan sampling design.