Precision enhancement in variance estimation for complex environmental populations using adaptive cluster sampling.

Area of Science:

• Statistics
• Survey Methodology
• Ecological Sampling

Background:

• Estimating population parameters for rare, clustered, and inaccessible populations presents significant statistical challenges.
• Conventional sampling methods often result in overestimated variance, failing to accurately represent population dispersion.
• Adaptive cluster sampling (ACS) is recognized for its efficiency in reducing variance for such populations.

Purpose of the Study:

• To introduce a generalized estimator for variance estimation in rare, hidden, geographically clustered, and hard-to-reach populations.
• To leverage both actual and transformed auxiliary data within the framework of adaptive cluster sampling.
• To provide a more precise estimation of population variance compared to existing methods.

Main Methods:

• Development of a generalized variance estimator incorporating auxiliary data.
• Application of adaptive cluster sampling principles.
• Derivation of approximate bias and mean square error using first-order Taylor expansion.
• Validation through simulation studies and real-world data applications.

Main Results:

• The proposed generalized estimator effectively utilizes auxiliary information, both raw and transformed.
• The method demonstrates improved precision in variance estimation for challenging population types.
• Analytical expressions for bias and mean square error were derived, confirming theoretical properties.

Conclusions:

• The novel generalized estimator offers a more accurate approach to variance estimation for rare and clustered populations.
• Integrating auxiliary data with adaptive cluster sampling enhances estimation efficiency.
• The findings have implications for ecological studies, resource management, and other fields dealing with difficult-to-sample populations.