Enhancing variance estimation in adaptive cluster sampling using exponential estimators with auxiliary information...

Area of Science:

• Ecology and Wildlife Management
• Statistical Methods in Ecology
• Population Dynamics

Background:

• Accurate variance estimation is crucial for wildlife population assessments.
• Traditional sampling methods may lack efficiency for certain ecological populations.
• Auxiliary information can potentially improve estimation accuracy.

Purpose of the Study:

• To improve variance estimation for African hartebeest populations.
• To develop and evaluate novel exponential estimators using adaptive cluster sampling.
• To enhance the accuracy of population estimates through auxiliary variable utilization.

Main Methods:

• Adaptive cluster sampling methodology was employed.
• Several modified exponential estimators were proposed using different auxiliary variables.
• Bias and mean squared error were derived using Taylor and exponential expansions.
• A generalized exponential estimator was formulated to unify proposed estimators.
• Numerical and simulation studies were conducted using African hartebeest data.

Main Results:

• The proposed modified exponential estimators demonstrated improved accuracy.
• The generalized exponential estimator provided a unified framework with effective special cases.
• Mathematical comparisons showed the superiority of the generalized estimator over existing methods.
• Empirical evaluations using real African hartebeest data confirmed the efficacy of the proposed estimators.

Conclusions:

• The developed exponential estimators significantly enhance variance estimation for African hartebeest populations.
• Adaptive cluster sampling combined with auxiliary information offers a robust approach for wildlife population studies.
• The findings provide valuable statistical tools for ecological research and conservation efforts.