(1) Applied Statistics unit, Indian Statistical Institute, 203 B.T. Road, Kolkata, India;(2) Directorate General of Mines Safety, Dhanbad, Jharkhand, 826001, India
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