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 are developed using the Jackknife resampling technique, which is employed to enhance the performance of ratio-type estimators. Theoretical properties, including bias and mean square error (MSE), are derived, and a simulation study is conducted to validate the theoretical findings. Results demonstrate that the proposed estimators consistently outperform conventional estimators that do not utilize auxiliary variables across all network sample sizes. Furthermore, in several scenarios, the proposed estimators also exhibit superior efficiency compared to existing ratio estimators that do incorporate auxiliary information.