Estimating the population mean using a complex sampling design dependent on an auxiliary variable - Arijit Chaudhuri; Sonakhya Samaddar (Statistics in Transition new series (SiTns), 2022)
In surveying finite populations, the simplest strategy to estimate a population total with- out 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 Replace- ment (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.
Keywords: 519; 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