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  • Comparison of Variance Estimators of the Horvitz-Thompson Estimator for Randomized Variable Probability Systematic Sampling
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  • https://doi.org/10.1080/01621459.1994.10476443Copy DOI Icon

Comparison of Variance Estimators of the Horvitz-Thompson Estimator for Randomized Variable Probability Systematic Sampling

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Abstract

Abstract The National Stream Survey (NSS) and Environmental Monitoring and Assessment Program (EMAP) use variable probability, systematic sampling, and the Horvitz-Thompson estimator to estimate population parameters of ecological interest. A common strategy of variance estimation for systematic sampling is to assume that the population order had been randomized prior to sampling and to estimate variance under this randomized population model. The Yates-Grundy variance estimator is generally recommended for estimating the variance of the Horvitz-Thompson estimator under this model. But design features of NSS and EMAP preclude application of the Yates-Grundy estimator, so use of the Horvitz-Thompson variance estimator is required. Further, because the first-order inclusion probabilities are known only for the sample units and not the entire population, neither the actual pairwise inclusion probabilities (πuv's) nor the Hartley-Rao approximation of the πuv's can be computed. Thus the variance estimator prop...

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