On two properties of an unequal probability sampling scheme |
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Authors: | Dr Arun Kumar Adhikary Dr Arijit Chaudhuri |
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Institution: | (1) Indian Statistical Institute, 203, Barrackpore Trunk Road, 700035 Calcutta |
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Abstract: | Summary For an inclusion probability proportional to size (IPPS) sampling scheme recently proposed by Saxena, Singh and Srivastava
(1986), it is shown that under certain simple verifiable conditions (1) the Horvitz-Thompson (1952) estimator based on it
has a smaller variance than the variance of the Hansen-Hurwitz (1943) estimator based on probability proportional to size
(PPS) sampling with replacement (WR) both involving the same size-measures and the expected sample size in the former being
equal to the number of draws in the latter and (2) the Yates-Grundy (1953) estimator for the variance of the Horvitz-Thompson
estimator based on this IPPS scheme is uniformly non-negative. |
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Keywords: | Efficiency Horvitz-Thompson estimator Inclusion probability proportional to size Non-negativity of variance estimator Probability proportional to size sampling |
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