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IMPROVEMENT OF PERFORMANCE OF VARIABLE PROBABILITY SAMPLING STRATEGIES THROUGH APPLICATION OF THE POPULATION SPACE AND THE FACSIMILE POPULATION BOOTSTRAP
Citation:
Overton, W. AND S. Stehman. IMPROVEMENT OF PERFORMANCE OF VARIABLE PROBABILITY SAMPLING STRATEGIES THROUGH APPLICATION OF THE POPULATION SPACE AND THE FACSIMILE POPULATION BOOTSTRAP. U.S. Environmental Protection Agency, Washington, D.C., EPA/620/R-94/011.
Description:
Performance of variable probability sampling designs depends on the relation of the response variable, y, to the auxiliary or design variable, x, which was used to select the sample. n particular, the Horvitz-Thompson estimator, a commonly used estimator of the population total in variable probability sampling, perfo3.,ms well (in terms of precision) when the relation of y to x is linear and passes through the origin. n many surveys, the auxiliary design variable is selected to optimize estimation of the most important response variable. hen several response variables are of interest, some response variables will have a relation to x that results in poor precision of the Horvitz-Thompson estimator. n other surveys, variable probability sampling results from necessity, rather than being selected for the objective of optimizing precision. his situation often arises in sampling ecological resources, and EMAP provides an excellent example. n this case, the relation of many response variables to the design variables is expected to be such that the Horvitz-Thompson estimator will have low precision for those response variables. everal suggestions have been made to improve the analysis of such surveys. n this paper, the authors explore design-based inference under variable probability sampling in which the inclusion probabilities, are proportional to the auxiliary (design) variable x. we denote this design as px, for inclusion probability proportional to x.