Large scale surveys very often involve multi-stage sampling design, where the first-stage units are selected with varying probability sampling
without replacement method and the second and subsequent stages units are selected with varying or equal probability sampling schemes. It is well known (vide Chaudhuri and Arnab (1982)) that for such sampling designs it impossible to find an unbiased estimator of the variance of the estimator of the population total (or mean) as a homogeneous quadratic function of the estimators of the totals (means) of second-stage units without estimating variances of the estimators of the totals (means) of the second and sub-sequent stages of sampling. Wolter (1985) has shown that the Jackknife estimators of the population total based on unequal probability sampling overestimates the variance. In this paper we have proposed an alternative Jackknife estimator after reduction of bias from the original Jackknife estimator. The performances of the proposed Jackknife estimator and the original estimator are compared through simulation studies using Household Income and Expenditure Survey (HIES) 2002/03 data collected by CSO, Botswana. The simulation studies reveal that the proposed estimator fares better than the original Jackknife estimator in terms of relative bias and mean-square error.
Complex survey design, Inclusion probability proportional to size, Jackknife estimator, Variance estimation, Varying probability sampling