Abstract
A formula is presented for an unbiased estimator for the variance of an unbiased estimator of a survey population total as well as for an unbiased estimator of its variance based on sampling in two-stages following Rao et al. J Roy Stat Soc B 24: 482–491 (1962) scheme in both stages when the originally selected units in both stages cannot be fully covered in the survey but are to be randomly sub-sampled. The development is helpful to tackle non-responses if assumed to have occurred at random in either or both the stages
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References
Chaudhuri A, Adhikary AK, Dihidar S (2000) Mean square error estimation in multi-stage sampling. Metrika 52(2):115–131
Rao JNK, Hartley HO, Cochran WG (1962) On a simple procedure of unequal probability sampling without replacement. J Roy Stat Soc B 24:482–491
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Chaudhuri, A., Saha, A. Estimation from two-stage unequal probability sampling with missing units. Metrika 63, 33–41 (2006). https://doi.org/10.1007/s00184-005-0004-0
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DOI: https://doi.org/10.1007/s00184-005-0004-0