Application of Midzuno Scheme in Adaptive Cluster Sampling
This paper proposes an adaptive cluster sampling using unequal probability without replacement for selecting an initial sample. Midzuno scheme was applied for selecting an initial sample in adaptive cluster sampling. Two unbiased estimators of the population total are proposed. The variances of the proposed estimators and their unbiased estimators were also derived. A small population was also used to show the unbiased property of the estimators under the proposed sampling design. The simulation study was used to compare the efficiency of the proposed sampling design to the original adaptive cluster sampling. The auxiliary variable is created to construct the initial probability. The coefficient of correlation between the study variable and auxiliary variable consists of 0.3, 0.5, 0.7 and 0.9. The results showed that the proposed sampling design was more efficient than the original adaptive cluster sampling. In particular, when the correlation coefficient between the auxiliary and the study variables increases, the proposed sampling scheme was more efficient. In addition, the units in the initial sample are easy to draw and the proposed estimates are easy to compute.