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Inference on data with both multiplicative and additive measurement errors
Yuxiang Zong1, Yinfu Liu2, Yanyuan Ma3
1Research Centre for Operations Research and Statistics, KU Leuven, Naamsestraat 69, 3000 Leuven, Belgium.
Summary
This study addresses measurement errors in statistical analysis, proposing a new method to identify and estimate both additive and multiplicative errors. The approach enhances statistical accuracy in various applications.
Area of Science:
- Statistics
- Econometrics
- Biostatistics
Background:
- Measurement errors are common in data analysis, often assumed as additive or multiplicative.
- Existing methods may not fully capture complex error structures.
Purpose of the Study:
- To develop a statistical method for identifying and estimating variables with both additive and multiplicative measurement errors.
- To assess the impact of these errors on linear regression parameter estimation.
Main Methods:
- Proposed a moment-based estimator for error variances.
- Derived the asymptotic distribution and developed hypothesis tests for error existence.
- Utilized a likelihood-based approach for density approximation.
- Integrated methods with Regression Calibration and Simulation Extrapolation for linear regression.
Main Results:
- Established identifiability of additive and multiplicative errors.
- The proposed moment-based estimator is consistent.
- Asymptotic distribution derived for hypothesis testing.
- Methodology evaluated through simulations and a real data application.
Conclusions:
- The study provides a robust framework for handling combined additive and multiplicative measurement errors.
- The proposed methods improve the accuracy of statistical analysis and regression parameter estimation.
- The approach is validated for practical use in real-world data scenarios.
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