In surveying finite populations, the simplest strategy to estimate a population total without bias is to employ Simple Random Sampling (SRS) with replacement (SRSWR) and the expansion estimator based on it. Anything other than that including SRS Without Replacement (SRSWOR) and usage of the expansion estimator is a complex strategy. We examine here (1) if from a complex sample at hand a gain in efficiency may be unbiasedly estimated comparing the ”rival population total-estimators” for the competing strategies and (2) how suitable model-expected variances of rival estimators compete in magnitude as examined numerically through simulations.

Des Raj and symmetrized Des Raj estimator and associated variance, Hansen- Hurwitz estimation and variance, Hartley-Ross, Horvitz-Thompson, Lahiri-Midzuno-Sen, Murthy, Rao-Hartley-Cochran procedures vis-a-vis SRSWOR and SRSWR

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