ABSTRACT
A sampling design or equivalently a sampling scheme coupled with a method of estimation should yield an estimator for a finite population total or mean with a bias small in magnitude and a Mean Square Error (MSE) also small enough. By employing simple random sampling with or without replacement an exactly unbiased estimator for a population mean or total is assured. J. N. K. Rao and Hajek approach of deriving 'necessary conditions' for uniform non-negativity of unbiased estimators for the MSE of a homogeneous linear estimator for a finite population total. Probability proportional to size with replacement sampling suffers from the obvious shortcoming that the units chosen may not be distinct. Subsequent draws producing units already drawn, if surveyed do not yield additional data and hence no fresh information. Use of a ratio estimator for a finite population total or a mean is very popular.
