Modifications on re-scaling bootstrap for adaptive sampling

In complex survey design, the resampling method is often used for assessing the variability and confidence interval of non-linear estimators which is a function of several estimated means or totals. A well-known resampling method, called the re-scaling bootstrap technique was originated by Rao and Wu (1988). This article is an attempt to propose a re-scaling bootstrap technique in estimating the parameters of rare and clustered population for a complex survey design. Adaptive cluster sampling design is a probabilistic approach to reach out to the rare and clustered units. Thompson (1990) introduced this design. Chaudhuri (2000) extended this design for varying probability sampling. In practice, the final sample size of adaptive sampling may be exorbitantly large. From this realistic point of view, Chaudhuri, Bose, and Dihidar (2005) developed the size-constrained adaptive sampling design, in varying probability sampling. We first describe here, how this well-known re-scaling bootstrap technique may be employed for non-linear estimators of the population total, in the case of rare and clustered population. It has been found that there is a need to develop an alternative re-scaling bootstrap procedure to avoid complications in computation to cover Chaudhuri, Bose, and Dihidar (2005). A simulation study has been carried out to demonstrate the proposed methods.