it is proved in this paper that under the assumption of a super-population model.the precision of 3P sampling with a ratio estimator is asymptotically equal to the precision of πPSWor sampling with Horvitz-Thompson estimator.
Yi Nengjun.
COMPARISON OF 3P SAMPLING WITH πPSWOR SAMPLING[J]. JOURNAL OF NANJING FORESTRY UNIVERSITY. 1995, 19(01): 98-101 https://doi.org/10.3969/j.jssn.1000-2006.1995.01.022
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