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Activity Number:
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293
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Type:
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Contributed
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Date/Time:
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Tuesday, August 8, 2006 : 10:30 AM to 12:20 PM
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Sponsor:
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Section on Survey Research Methods
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| Abstract - #306919 |
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Title:
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A Matrix Approach for Comparing Estimates of a Population Total under a Many-to-Many Frame Structure
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Author(s):
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Martin Levy and ZhiYuan Dong*+
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Companies:
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University of Cincinnati and University of Cincinnati
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Address:
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P.O. Box 210130, Cincinnati, 45221,
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Keywords:
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imperfect frames ; correspondence errors ; weighting ; simple random sampling ; quadratic forms
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Abstract:
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We compare population total estimator precision under simple random sampling when frame units and population elements have a many-to-many correspondence. Three methods that adjust for multiplicities are: perfect the frame and use standard estimation methods (PF); adjust for imperfections using either Arc-Weight (AW), or Horvitz-Thomson (HT) estimators. We represent the underlying structure as a bipartite graph and express the variances of PF, HT, and AW as quadratic forms depending on the graph's incidence matrix permitting data-free dominance studies. We show that AW is a close relative to HT when AW is viewed using a new tool, the First Order Inclusion-Weight. A comprehensive search algorithm is developed to enumerate all non-isomorphic bipartite graphs associated with any feasible valence settings to investigate all systems of "small" size and identify non-trivial dominance results.
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