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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.

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Summary
This summary is machine-generated.

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.

Keywords:
Bernstein polynomialMeasurement errorMethod of momentsRegression calibrationSimulation extrapolation

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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.