A comparison of conditional Poisson sampling versus unequal probability sampling with replacement
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Journal of Statistical Planning and Inference
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The variance of the Horvitz–Thompson estimator for a fixed size ConditionalPoissonsampling scheme without replacement and with unequal inclusion probabilities is compared to the variance of the Hansen–Hurwitz estimator for asampling scheme with replacement. We show, using a theorem by Gabler, that the sampling design without replacement is more efficient than the sampling design with replacement.
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