A Cautionary Note on the Hanurav–Vijayan Sampling Algorithm. (5th April 2022) - Chauvet, Guillaume
Abstract: We consider the Hanurav–Vijayan (HV) 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 (HT) estimator is not generally consistent under this sampling design. We propose a conditional HT estimator and prove its consistency under a nonstandard assumption on the first-order inclusion probabilities. Since this assumption seems difficult to control in practice, we recommend not to use the HV sampling design.