On some properties of variable size simple random sampling and a limit theorem
Tommy Wright · Communication in Statistics- Theory and Methods · 1988
This paper introduces a sampling plan for finite populations herein called “variable size simple random sampling” and compares properties of estimators based on it with results from the usual fixed size simple random sampling without replacement. Necessary and sufficient conditions (in the spirit of Hajek (1960)) for the limiting distribution of the sample total (or sample mean) to be normal are given.