  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.
