Enhanced Ratio-Type Estimators in Adaptive Cluster Sampling Using Jackknife Method

Adaptive cluster sampling is a methodology designed for data collection in contexts where the population is rare and spatially clustered. This approach has been effectively applied in various disciplines, including epidemiology and resource management. The present study introduces novel estimators that incorporate auxiliary variable information to improve estimation efficiency. These estimators were developed using the jackknife resampling technique to improve the performance of ratio-type estimators. Theoretical properties, including bias and mean square error (MSE), were derived, and a simulation study was conducted to validate the theoretical findings. The results demonstrated that the proposed estimators consistently outperformed conventional estimators that do not utilize auxiliary variables across all network sample sizes. Furthermore, in several scenarios, the proposed estimators also exhibited superior efficiency to existing ratio estimators that do incorporate auxiliary information.