How can survey researchers obtain more accurate population estimates when useful auxiliary information becomes available after sampling?
This study proposes an improved ratio-type exponential estimator for estimating a finite population mean under post-stratification.
In this approach, a simple random sample is first selected and then divided into post-strata using relevant auxiliary variables. The estimator combines information on the study variable with additional data from the post-stratification process to reduce estimation error.
The researchers mathematically derived the estimatorโs bias and mean squared error and established the conditions under which it is more efficient than the usual unbiased estimator, the classical ratio estimator, and an existing exponential estimator.
Its practical performance was tested using a real dataset containing information on industrial output, fixed capital, and number of workers across two post-strata.
The proposed estimator recorded the lowest mean squared error of 3182.05, compared with 3558.77 for the existing exponential estimator, 9867.27 for the classical ratio estimator, and 10059.07 for the unbiased estimator.
It also achieved the highest percentage relative efficiency of 316.12%, representing an efficiency improvement of more than 210% over the classical ratio estimator.
Although its relative bias was slightly higher than that of some competing estimators, the value remained very small. Its superior overall performance resulted mainly from a substantial reduction in variance.
The findings demonstrate that the proposed estimator can provide more precise and reliable population-mean estimates, particularly in surveys where relevant auxiliary information is available and populations can be meaningfully divided into post-strata.
This method offers survey researchers and statisticians a practical tool for improving estimation accuracy in demographic, economic, agricultural, industrial, and other population-based studies.
๐ Read the full article here:
https://doi.org/10.46481/asr.2026.5.2.479
Published in: African Scientific Reports