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A general class of improved population variance estimators under non-sampling errors using calibrated weights in
M K Pandey1, G N Singh2, Tolga Zaman3
1Department of Mathematics and Computing, Indian Institute of Technology (Indian School of Mines), Dhanbad, 826004, India. maheshbabu3797@gmail.com.
Scientific Reports
|February 5, 2024
Summary
This study introduces a new calibration estimator for population variance in stratified two-phase sampling, addressing non-response and measurement errors. The proposed method improves variance estimation accuracy, particularly for gas turbine data.
Area of Science:
- Statistics
- Survey Methodology
- Engineering Data Analysis
Background:
- Estimating population variance in complex survey designs presents challenges.
- Non-response and measurement errors can significantly bias variance estimates.
- Stratified two-phase sampling is a common but intricate survey design.
Purpose of the Study:
- To develop a novel calibration estimator for population variance.
- To account for random non-response and measurement errors in stratified two-phase sampling.
- To apply and validate the proposed method using gas turbine exhaust pressure data.
Main Methods:
- Development of a general class of calibration estimators.
- Integration of auxiliary variables with high positive correlation.
- Derivation of calibrated strata weights.
- Analysis of biases and mean square errors through theoretical examination and simulation studies.
Main Results:
- The proposed calibration estimators demonstrate superior performance compared to the natural estimator.
- Numerical and simulation studies confirm the efficiency and robustness of the new estimators.
- The method effectively handles non-response and measurement errors in variance estimation.
Conclusions:
- The new calibration estimator offers a more accurate approach to estimating population variance in stratified two-phase sampling.
- The findings provide practical tools for survey statisticians dealing with complex data.
- Recommendations are provided for applying these advanced estimation techniques in real-world scenarios.
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