Comparison of Four Estimators under sampling without Replacement

Abstract

In some applications, it is cost efficient to sample data in more than one stage. In the first stage, a simple random sample is drawn and then stratified accordingly to some easily measured attributes. This project described four estimators for the treatment of samples drawn without replacement when equal and unequal probabilities are considered. It also compared their resulting standard error under sampling without  replacement using data on diabetic patients in Niger state for the years 2000, 2001, 2002 and 2003. The results were obtained using a program written in Microsoft Visual C++ programming language. It was observed that the two-stage sampling under unequal probabilities without replacement is always better than the other three estimators considered.

Keywords: Unequal probability sampling, two-stage sampling, hansen-hurwitz estimator and horvitz-thompson estimator.