Modified correlated measurement errors model for estimation of population mean utilizing auxiliary information

Area of Science:

• Statistics
• Statistical Modeling
• Survey Sampling

Background:

• Measurement errors are inherent in practical data collection and can degrade the performance of statistical estimators.
• Existing correlated measurement error models, such as the one by Shalabh and Tsai (2017), have limitations in certain applications.
• The need for robust estimation techniques that account for measurement errors is critical in statistical inference.

Purpose of the Study:

• To propose a modified correlated measurement errors model.
• To develop novel ratio and product estimators for population mean estimation under this new model.
• To assess the efficiency of the proposed estimators compared to existing ones.

Main Methods:

• Development of modified ratio and product estimators for population mean.
• Analysis of estimator properties using simple random sampling without replacement (SRSWOR).
• First-order approximation for theoretical efficiency comparisons.
• Empirical study to validate theoretical findings.

Main Results:

• The proposed ratio and product estimators demonstrate improved efficiency over the conventional unbiased estimator.
• The new estimators outperform the Shalabh and Tsai (2017) ratio and product estimators under realistic conditions.
• Empirical evidence supports the superiority of the developed estimators.

Conclusions:

• The modified correlated measurement errors model provides a better framework for estimation in the presence of measurement errors.
• The newly developed ratio and product estimators offer significant efficiency gains.
• The findings are particularly relevant for survey sampling where measurement errors are common.