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Generalization of HT strategy and its application. (English) Zbl 0779.62011

The Horvitz-Thompson strategy (HT-strategy) can be generalized by redefining the so-called inclusion probabilities so that estimators and their variance formulas for both with-replacement sampling and without- replacement sampling are represented in the same forms. Using this result we can find a feasible procedure which improves a given strategy of with- replacement sampling to a better strategy of without-replacement sampling under suitable conditions.
Necessary and sufficient conditions for existence of a sampling design are obtained, which induce the first-order or second-order inclusion probabilities given in advance, in the case of without-replacement sampling designs.

MSC:

62D05 Sampling theory, sample surveys
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