Optimizing population mean estimation in stratified sampling using linear cost: A simulation study

Area of Science:

• Statistics
• Survey Methodology
• Applied Mathematics

Background:

• Improving sampling efficiency is a persistent challenge.
• Simultaneously enhancing estimator efficacy and optimizing survey costs is crucial in fields like medicine, agriculture, and transportation.

Purpose of the Study:

• To develop a family of generalized exponential estimators for population mean estimation in stratified sampling.
• To optimize survey costs using integer programming and Lagrange multipliers within a fixed budget.

Main Methods:

• Derivation of the Mean Square Error (MSE) for proposed estimators.
• Formulation of an optimization problem to refine estimator performance under cost constraints.
• Utilization of integer programming and Lagrange multipliers for cost optimization.

Main Results:

• Proposed generalized exponential estimators significantly outperform existing alternatives.
• Theoretical and empirical evaluations confirm the superiority of the new estimators.
• Demonstrated practical relevance and theoretical robustness through real-world dataset validation.

Conclusions:

• The developed estimators offer a robust and efficient solution for stratified sampling.
• The methodology effectively balances estimator performance with survey cost optimization.
• Findings have broad applicability across various data collection domains.