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Abstract:
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We extend our matrix approach for comparing the precision of an estimator of a population total under a many-to-many frame structure to the case of stratified random sampling. We investigate the key issue that arises in this design, which is called cross-over, to make it expressible in matrix terms via two methods, one involving decomposition, the other involving a new arc-weight estimator. The stratified case is made tractable by integrating it into our current matrix notation for the SRSWOR case so that we can characterize both the estimates of the population total and their variances under a perfect frame, and using the Horvitz-Thomson and the Arc-Weight estimators under an imperfect frame. We develop code to implement the decomposition of the parent imperfect frame system into closed sub-systems and reproduce the decomposed system visually.
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