DefinePK

Research Objective

To propose a family of exponential-type estimators for the unspecified population mean when survey data is affected by measurement error in both the study and auxiliary variables, and to evaluate its performance against existing estimators.

Methodology

The study proposes a generalized family of exponential-type estimators. Theoretical expressions for bias and mean square error (MSE) are derived up to the first-order approximation. Efficiency comparisons are made with existing estimators. Numerical and simulation studies are conducted using R, with data generated from bivariate normal distributions and a real-life dataset. Percent relative efficiencies (PREs) are calculated with respect to the ordinary mean estimator.

Methodology Flowchart

                        graph TD
    A["Define Problem: Population Mean Estimation with Measurement Error"] --> B["Develop Generalized Family of Exponential-Type Estimators"]
    B --> C["Derive Theoretical Expressions for Bias and MSE"]
    C --> D["Define Notations and Existing Estimators"]
    D --> E["Conduct Theoretical Efficiency Comparison"]
    E --> F["Perform Simulation Study using R"]
    F --> G["Conduct Numerical Study with Real-life Data"]
    G --> H["Analyze Results: MSE and PRE"]
    H --> I["Compare Proposed Estimators with Existing Ones"]
    I --> J["Draw Conclusions and Discuss Implications"]                    

Discussion

The research highlights the significant impact of measurement errors on the efficiency of statistical estimators. The proposed family of estimators offers a robust solution for situations where both the study and auxiliary variables are subject to measurement errors. The study emphasizes the importance of accounting for measurement errors in survey design and analysis to ensure accurate statistical inferences.

Key Findings

The proposed generalized family of exponential-type estimators performs best compared to similar existing estimators in the presence of measurement error across all tested populations. The efficiency of the recommended estimator decreases when measurement error is considered. The suggested estimators show increased PREs with increasing correlation coefficients between auxiliary and study variables.

Conclusion

A generalized family of exponential-type estimators has been successfully developed and validated for estimating the finite population mean in the presence of measurement errors. The proposed estimators demonstrate superior performance and efficiency compared to existing methods, underscoring the necessity of addressing measurement errors in statistical surveys.

Fact Check

1. The paper is published in the Journal of Statistics, Volume 28, 2024, pages 30-45. (Confirmed by the header information).
2. The study uses R for simulation studies, averaging results over 10,000 iterations. (Confirmed in Section 6).
3. The numerical study uses data from Gujarati & Sangeetha (2007) for true and measured consumption expenditure and income. (Confirmed in Section 7).

Mind Map